Download Geometry v. 2016

2015 - 2016
Geometry
This course offers a thorough introduction to the basic concepts of plane (Euclidean) geometry through a
series of conjectures and formal proofs. Prisms, Pyramids, cylinders, cones and spheres as well as an
introduction to applied trigonometry are also included. Much emphasis is placed on the application of algebra
skills.
Course Information:
Frequency & Duration: Daily for 42 minutes
Text: Pearson Geometry Common Core (2012)
Mathematics: Geometry
Content: Tools of Geometry
v. 2015 - 2016
Duration: Aug./ Sept. (3 weeks)
Essential What are the building blocks of Geometry?
Question:
Skill:
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Understand basic terms and postulates of geometry.
Find and compare lengths of segments and the measures of angles.
Identify special angle pairs and use them to find angle measures.
Use a straightedge and compass to make basic constructions.
Use distance and midpoint formulas when given 2 points in the coordinate plane.
Find the perimeter, circumference, and/or area of basic shapes.
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Use a compass and a straightedge to bisect angle ABC.
Using a diagram of a plane, lines, and points, name 3 collinear points, 4 coplanar points, and the
intersection of a line and a plane.
Find the perimeter of triangle ABC with vertices A(-2,8), B(3,13), and C(14,2).
Find the area of a circle with diameter 9 cm.
The intersection of two planes is a point? (True or false?)
LJ and TJ are opposite rays. (True or false?)
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Resources: Pearson Geometry Common Core: Chapter 1, pages 1-75
Standards:
CC.2.3.HS.A.11- Apply coordinate geometry to prove simple geometric theorems algebraically.
CC.2.3.8.A.2- Understand and apply congruence, similarity, and geometric transformations using various
tools.
CC.2.3.HS.A.3-Verify and apply geometric theorems as they relate to geometric figures.
Vocabulary:
Angle bisector- is a ray that divides an angle into two congruent angles; Congruent segmentssegments that have the same length; Construction- is a geometric figure made with only a straightedge
and compass; Linear pair- a pair of adjacent angles whose non-common sides are opposite rays;
Perpendicular bisector- is a line, segment, or ray that is perpendicular to the segment at its midpoint;
Postulate- is an accepted statement of fact; Supplementary angles- two angles whose sum is 180
degrees; Segment bisector- a line, segment, ray, or plane that intersects a segment at its midpoint;
Vertical angles- two angles whose sides form two pairs of opposite rays
Comments:
Mathematics: Geometry
Content: Reasoning and Proof
v. 2015 - 2016
Duration: September/ October (3 weeks)
Essential How can you make a conjecture and prove that it is true?
Question:
Skill:
Assessment:
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Use inductive reasoning to make conjectures.
Recognize conditional statements.
Write converses, inverses, and contrapositives of conditionals.
Use deductive reasoning to reach a conclusion.
Connect reasoning in Algebra and Geometry.
Prove and apply theorems about angles.
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Explain the difference between inductive and deductive reasoning.
What is a counterexample?
Find the next two terms of: -16, 8, -4, 2, …
Identify the hypothesis and conclusion of: If x + 9 = 11, then x = 2.
The measure of an angle is 52 more than the measure of its complement. What is the measure of
the angle?
Resources: Pearson Geometry Common Core: Chapter 2, pages 79-133
Standards:
Vocabulary:
Comments:
CC.2.3.HS.A.3--Verify and apply geometric theorems as they relate to geometric figures.
Conditional- is an if-then statement; Conjecture- a conclusion reached by using inductive reasoning;
Converse- a statement obtained by reversing the hypothesis and conclusion of a conditional; CoTheorem- is a conjecture that can be proven; Deductive reasoning- a process of reasoning logically
from given facts to a conclusion; Inductive reasoning- a type of reasoning that reaches conclusions
based on a pattern of specific examples or past events
Mathematics: Geometry
Content: Parallel and Perpendicular Lines
v. 2015 - 2016
Duration: October (3 weeks)
Essential How do you prove that two lines are parallel, perpendicular, or neither?
Question:
Skill:
Assessment:
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Identify relationships between figures in space.
Identify angles formed by two lines and a transversal.
Prove theorems about parallel lines.
Use properties of parallel lines to find angle measures.
Use parallel lines to prove a theorem about triangles.
Find measures of angles of triangles.
Construct parallel and perpendicular lines.
Graph and write linear equations.
Relate slope to parallel and perpendicular lines.
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x and 20 are two angle measures of a triangle. What is the measure of the third angle?
Write the definition and draw a diagram of each: skew lines, parallel lines, and perpendicular lines.
Write an equation of a line that passes through (1, 5) and (3, -13).
If the slope of a line is m = 1.5, then the slope of another line that is perpendicular would be?
Draw a diagram of two parallel lines cut by a transversal and then identify a pair of: alternate interior
angles, alternate exterior angles, corresponding angles, and same-side interior angles.
Resources: Pearson Geometry Common Core: Chapter 3, pages 140-211
Standards: CC.2.3.HS.A.11- Apply coordinate geometry to prove simple geometric theorems algebraically.
Parallel lines- lines that lie in the same plane and never intersect; Skew lines- lines that do not lie in the
Vocabulary: same plane; Transversal- a line that intersects two or more lines at distinct points.
Comments:
Mathematics: Geometry
Content: Congruent Triangles
v. 2015 - 2016
Duration: November (3 weeks)
Essential How do you prove that two triangles are congruent?
Question:
Skill:
Assessment:
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Recognize congruent figures and their corresponding parts.
Use SSS, SAS, ASA, AAS, or HL to prove that triangles are congruent.
Use CPCTC to prove that corresponding parts of congruent triangles are congruent.
Use and apply properties of isosceles and equilateral triangles.
Identify congruent overlapping triangles.
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What are the 5 tests that we have learned in order to prove that triangles are congruent?
Triangle CEO is congruent to triangle HDF. Name all of the pairs of corresponding congruent
parts.
In triangle HFD, what angle is included between DH and DF?
When do you use CPCTC?
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Resources: Pearson Geometry Common Core: Chapter 4, pages 218-277
CC.2.3.HS.A.3--Verify and apply geometric theorems as they relate to geometric figures.
Standards:
Vocabulary:
Comments:
G.1.2.1-Recognize and/or apply properties of angles, polygons, and polyhedra.
G.1.2.1.1-Identify and/or use properties of triangles.
G.1.2.1.3-Identify and/or use properties of isosceles and equilateral triangles.
G.1.3.1-Use properties of congruence, correspondence, and similarity in problem-solving settings
involving two- and three-dimensional figures.
G.1.3.1.1-Identify and/or use properties of congruent and similar polygons or solids.
Base angles of an Isosceles triangle- the angles opposite the legs of an isosceles triangle; Congruent
polygons- polygons that have the same size and the same shape; Corollary- a theorem that can be
proved easily using another theorem; Hypotenuse- in a right triangle, the side that is opposite the right
angle; Vertex angle of an Isosceles triangle- the angle that is opposite the base of an isosceles triangle
Mathematics: Geometry
Content: Relationships Within Triangles
v. 2015 - 2016
Duration: December (3 weeks)
Essential How do you solve problems that involve measurements of triangles and how do you use coordinate
Question: geometry to find relationships within triangles?
Skill:
Assessment:
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Use properties of mid-segments to solve problems.
Use properties of perpendicular bisectors and angle bisectors.
Identify properties of perpendicular bisectors and angle bisectors.
Identify properties of medians and altitudes of a triangle.
Use indirect reasoning to write proofs.
Use inequalities involving angles and sides of triangles.
Apply inequalities in two triangles.
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Find the coordinates of the circumcenter of triangle ABC given A(3, -1), B(-2, -1), and C(3, -8).
Find the coordinates of the orthocenter of triangle DEF given D(-1, -1), E(-1, -5), and F(-4, -1).
If AB = 9, BC = 4.5, and AC = 12, list the angles of triangle ABC from smallest to largest.
Describe a centroid of a triangle.
Resources: Pearson Geometry Common Core: Chapter 5, pages 285-345
CC.2.3.HS.A.11- Apply coordinate geometry to prove simple geometric theorems algebraically
Standards:
G.1.2.1-Recognize and/or apply properties of angles, polygons, and polyhedra.
G.1.2.1.1-Identify and/or use properties of triangles.
G.1.2.1.3-Identify and/or use properties of isosceles and equilateral triangles.
CC.2.3.HS.A.3--Verify and apply geometric theorems as they relate to geometric figures.
G.1.3.2-Write formal proofs and/or use logic statements to construct or validate arguments.
G.1.3.2.1-Write, analyze, complete, or identify formal proofs.
G.2.1.2-Solve problems using analytical geometry.
G.2.1.2.1-Calculate the distance and/or midpoint between two points on a number line or on a
coordinate plane.
G.2.1.2.2-Relate slope to perpendicularity and/or parallelism.
G.2.1.2.3-Use slope, distance, and/or midpoint between two points on a coordinate plane to establish
properties of a two-dimensional shape.
G.2.2.1-Use and/or compare measurements of angles.
G.2.2.1.2-Use properties of angles formed when two parallel lines are cut by a transversal to find the
measures of missing angles.
Mathematics: Geometry
Vocabulary:
Comments:
v. 2015 - 2016
Altitude of a triangle- is the perpendicular segment from a vertex to the line containing the side
opposite that vertex; Centroid of a triangle- is the point of concurrency of the medians of the triangle;
Circumcenter of a triangle- is the point of concurrency of the perpendicular bisectors of the sides of
the triangle; Concurrent lines- three or more lines that meet in one point; Distance from a point to a
line- the length of the perpendicular segment from the point to the line
Mathematics: Geometry
Content: Polygons and Quadrilaterals
v. 2015 - 2016
Duration: January (3 weeks)
Essential How can you classify quadrilaterals and how do you find the sum of the measures of polygon angles?
Question:
Skill:
Assessment:
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Find the sum of the measures of the interior angles of a polygon.
Find the sum of the measures of the exterior angles of a polygon.
Use relationships among sides and angles of parallelograms.
Use relationships among diagonals of parallelograms.
Determine whether a quadrilateral is a parallelogram.
Define and classify special types of parallelograms.
Use properties of diagonals of rhombuses and rectangles.
Determine whether a parallelogram is a rhombus or rectangle.
Verify and use properties of trapezoids and kites.
Classify polygons in the coordinate plane.
Name coordinates of special figures by using their properties.
Prove theorems using figures in the coordinate plane.
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What is the sum of the interior angle measures of a polygon with 17 sides?
What is the measure of an exterior angle of a 23-gon?
Determine the most precise name of quadrilateral ABCD when given: A(3, -2), B(5, 4), C(3, 6), and
D(1,4)
Prove that the diagonals of a square are congruent.
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Resources: Pearson Geometry Common Core: Chapter 6, pages 353-425
CC.2.3.HS.A.11- Apply coordinate geometry to prove simple geometric theorems algebraically.
Standards:
G.1.2.1-Recognize and/or apply properties of angles, polygons, and polyhedra.
G.1.2.1.2-Identify and/or use properties of quadrilaterals.
G.1.2.1.4-Identify and/or use properties of regular polygons.
CC.2.3.HS.A.3--Verify and apply geometric theorems as they relate to geometric figures.
G.1.3.2-Write formal proofs and/or use logic statements to construct or validate arguments.
G.1.3.2.1-Write, analyze, complete, or identify formal proofs.
G.2.1.2-Solve problems using analytical geometry.
G.2.1.2.1-Calculate the distance and/or midpoint between two points on a number line or on a
coordinate plane.
G.2.1.2.2-Relate slope to perpendicularity and/or parallelism.
G.2.1.2.3-Use slope, distance, and/or midpoint between two points on a coordinate plane to establish
properties of a two-dimensional shape.
Mathematics: Geometry
Vocabulary:
Comments:
v. 2015 - 2016
Equiangular polygon- polygon with all of its angles congruent; Equilateral polygon- polygon with all
of its sides congruent; Isosceles trapezoid- trapezoid with its legs congruent; Kite- quadrilateral with
two pairs of consecutive sides congruent; Parallelogram- quadrilateral with opposite sides parallel;
Rectangle- parallelogram with four right angles; Regular polygon- polygon that is both equilateral and
equiangular; Rhombus- parallelogram with four congruent sides; Square- parallelogram with four right
angles and four congruent sides; Trapezoid- quadrilateral with exactly one pair of parallel sides
Mathematics: Geometry
v. 2015 - 2016
Content: Similarity
Duration: February (3 weeks)
Essential How do you use proportions to find side lengths in similar polygons and how do you show two triangles
Question: are similar?
Skill:
Assessment:
Resources:
Standards:
Vocabulary:
Comments:
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Write ratios and solve proportions.
Identify and apply similar polygons.
Use AA, SAS, and SSS to prove that triangles are similar.
Use similarity to find indirect measurements.
Find and use relationships in similar right triangles.
Use the Side-Splitter Theorem and the Triangle-Angle-Bisector Theorem.
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What are similar figures?
Find the geometric mean between 5 and 12.
4
16
Solve:
=
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What three tests prove that triangles are similar?
𝑥+2
9
Pearson Geometry Common Core: Chapter 7, pages 432-483
CC.2.3.HS.A.6-Verify and apply theorems involving similarity as they relate to plane figures.
CC.2.3.HS.A.3--Verify and apply geometric theorems as they relate to geometric figures.
CC.2.3.HS.A.11- Apply coordinate geometry to prove simple geometric theorems algebraically.
CC.2.3.HS.A.14-Apply geometric concepts to model and solve real-world problems.G.1.3.1-Use
properties of congruence, correspondence, and similarity in problem-solving settings involving two- and
three-dimensional figures.
G.1.3.1.1-Identify and/or use properties of congruent and similar polygons or solids.
G.1.3.1.2-Identify and/or use proportional relationships in similar figures.
G.1.2.1-Recognize and/or apply properties of angles, polygons, and polyhedra.
G.1.2.1.1-Identify and/or use properties of triangles.
G.1.2.1.2-Identify and/or use properties of quadrilaterals.
G.1.2.1.3- Identify and/or use properties of isosceles and equilateral triangles.
Extended proportion- when three or more ratios are equal; Extended ratio- compares three or more
numbers; Extremes- the first and last numbers in a proportion; Means- the middle numbers in a
proportion; Proportion- two ratios that equal each other; Ratio- a comparison of two quantities by
division; Scale factor- the ratio of corresponding linear measurements of two similar figures; Similar
polygons- polygons with corresponding angles congruent and corresponding sides in proportion
Mathematics: Geometry
Content: Right Triangles and Trigonometry
v. 2015 - 2016
Duration: March (3 weeks)
Essential How do you find a side length or angle measure in a right triangle?
Question:
Skill:
Assessment:
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Use the Pythagorean Theorem and its converse.
Use properties of special right triangles.
Use sine, cosine, and tangent ratios.
Use angles of elevation and depression to solve problems.
Apply the Law of Sines.
Apply the Law of Cosines.
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Find the hypotenuse of a right triangle with side lengths 7 and 11.
Given triangle side lengths of 5 in., 6 in., and 10 in., identify the triangle as acute, right, or obtuse.
Sin A = ___
What is the mnemonic device that helps us remember the trigonometric ratios?
In triangle KLP, k = 13 mi, l = 10 mi, and p = 8 mi. Find the measure of angle K to the nearest
tenth.
Resources: Pearson Geometry Common Core: Chapter 8, pages 491-537
CC.2.2.HS.C.9-Prove the Pythagorean identity and use it to calculate trigonometric ratios.
CC.2.3.HS.A.3-Verify and apply geometric theorems as they relate to geometric figures.
CC.2.3.8.A.3-Understand and apply the Pythagorean theorem to solve problems.
CC.2.3.HS.A.11- Apply coordinate geometry to prove simple geometric theorems algebraically.
CC.2.3.HS.A.14- Apply geometric concepts to model and solve real-world problems.
Standards:
G.1.3.2.1-Write, analyze, complete, or identify formal proofs.
G.1.3.2-Write formal proofs and/or use logic statements to construct or validate arguments.
G.1.2.1.1-Identify and/or use properties of triangles.
G.1.2.1.3- Identify and/or use properties of isosceles and equilateral triangles.
G.1.2.1-Recognize and/or apply properties of angles, polygons, and polyhedra.
CC.2.3.HS.A.7-Apply trigonometric ratios to solve problems involving right triangles.
G.2.1.1.1-Use the Pythagorean theorem to write and/or solve problems involving right triangles.
G.2.1.1.2-Use trigonometric ratios to write and/or solve problems involving right triangles.
G.2.1.1-Solve problems involving right triangles.
G.2.1.2.1-Calculate the distance and/or midpoint between two points on a number line or on a
coordinate plane.
G.2.1.2.2-Relate slope to perpendicularity and/or parallelism.
G.2.1.2.3-Use slope, distance, and/or midpoint between two points on a coordinate plane to establish
properties of a two-dimensional shape.
G.2.1.2-Solve problems using analytical geometry.
Mathematics: Geometry
v. 2015 - 2016
Vocabulary: Pythagorean triple- a set of three nonzero whole numbers that satisfy the Pythagorean theorem
Comments:
Mathematics: Geometry
Content: Transformations
v. 2015 - 2016
Duration: April (3 weeks)
Essential What are the different types of transformations and how do they change a figures size and/or position?
Question:
Skill:
Assessment:
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Identify isometries.
Find translation images of figures.
Find reflection images of figures.
Draw and identify rotation images of figures.
Find compositions of isometries.
Classify isometries.
Identify congruence transformations.
Understand dilation images of figures.
Identify similarity transformations.
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Write the translation rule that maps P(-4, 2) to P’(-1, -1).
What transformations represent a rigid motion.
Is a dilation an isometry?
Find the image of A(2,3), B(-4,9), and C(-2,-4) after each transformation:
𝑅𝑥=4 (𝐴𝐵𝐶), 𝑇<−6,8> (𝐴𝐵𝐶), 𝑟(90°,𝑂) (𝐴𝐵𝐶), 𝐷3 (𝐴𝐵𝐶)
Resources: Pearson Geometry Common Core: Chapter 9, pages 545-607
Standards:
CC.2.3.HS.A.1- Use geometric figures and their properties to represent transformations in the plane.
CC.2.3.HS.A.2-Apply rigid transformations to determine and explain congruence.
CC.2.3.HS.A.5-Create justifications based on transformations to establish similarity of plane figures.
CC.2.3.HS.A.6--Verify and apply theorems involving similarity as they relate to plane figures.
CC.2.3.HS.A.3-Verify and apply geometric theorems as they relate to geometric figures.
CC.2.3.8.A.2- Understand and apply congruence, similarity, and geometric transformations using various
tools.
CC.2.3.8.A.2-Understand and apply congruence, similarity, and geometric transformations using various
tools.
CC.2.2.HS.C.1-Use the concept and notation of functions to interpret and apply them in terms of their
context.
G.1.3.1.1-Identify and/or use properties of congruent and similar polygons or solids.
G.1.3.1.2-Identify and/or use proportional relationships in similar figures.
G.1.3.1-Use properties of congruence, correspondence, and similarity in problem-solving settings
involving two- and three- dimensional figures.
G.2.1.2.1-Calculate the distance and/or midpoint between two points on a number line or on a
coordinate plane.
G.2.1.2-Solve problems using analytical geometry.
G.2.2.1-Use and/or compare measurements of angles.
Mathematics: Geometry
Vocabulary:
Comments:
v. 2015 - 2016
Dilation- an enlargement or reduction in the size of a figure; Image- is the resulting figure after a
transformation takes place; Isometry-a transformation in which an original figure and its image are
congruent; Rigid motion- a transformation that preserves distance and angle measure;
Transformation- any change made to a figures size, shape, and/or position; Translation- is a slide of a
geometric figure
Mathematics: Geometry
Content: Area
v. 2015 - 2016
Duration: April/May (3 weeks)
Essential How do you find the area of a polygon or find the circumference and area of a circle?
Question:
Skill:
Assessment:
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Find the area of parallelograms, triangles, trapezoids, rhombuses, kites, and regular polygons.
Find the perimeters and areas of similar polygons.
Find areas of regular polygons and triangles using trigonometry.
Find the measures of central angles and arcs.
Find the circumference and arc length.
Find the areas of circles, sectors, and segments of circles.
Use segment and area models to find the probabilities of events.
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What is the area of a right triangle with side lengths of 5, 12, and 13?
What is the area of a trapezoid with height 11 inches and bases 20 inches and 14 inches?
What is the area of a regular hexagon with a perimeter of 240cm?
If the ratio of the areas of two similar hexagons is 8:25, what is the ratio of their perimeters?
A circle has a radius of 20 cm. What is the area of the smaller segment of the circle formed by a 60
degree arc?
Resources: Pearson Geometry Common Core: Chapter 10, pages 616-681
CC.2.3.HS.A.8-Apply geometric theorems to verify properties of circles.
CC.2.3.HS.A.9-Extend the concept of similarity to determine arc lengths and areas of sectors of circles.
CC.2.3.HS.A.13-Analyze relationships between two-dimensional and three-dimensional objects.
CC.2.3.HS.A.3--Verify and apply geometric theorems as they relate to geometric figures.
Standards:
G.1.1.1.1-Identify, determine, and/or use the radius, diameter, segment, and/or tangent of a circle.
G.1.1.1.2-Identify, determine, and/or use the arcs, semicircles, sectors, and/or angles of a circle.
G.1.2.1-Recognize and/or apply properties of angles, polygons, and polyhedra.
G.2.2.2.1-Estimate area, perimeter, or circumference of an irregular figure.
G.2.2.2.2-Find the measurement of a missing length, given the perimeter, circumference, or area.
G.2.2.2.5-Find the area of a sector of a circle.
G.2.2.2-Use and/or develop procedures to determine or describe measures of perimeter, circumference,
and/or area.
G.2.2.3.1-Describe how a change in the linear dimension of a figure affects its perimeter, circumference,
and area.
G.2.2.3-Describe how a change in one dimension of a two-dimension figure affects other measurements
of that figure.
G.2.2.4.1-Use area models to find probabilities.
G.2.2.4-Apply probability to practical situations.
G.1.1.1.3
G.1.1.1
Mathematics: Geometry
Vocabulary:
Comments:
v. 2015 - 2016
Adjacent arcs- are arcs of the same circle that have one point in common; Apothem-is the
perpendicular distance from the center to a side of a regular polygon; Arc length-is a fraction of the
circumference; Central angle-an angle whose vertex is at the center of a circle; Circumference-the
distance around a circle; Concentric circles-coplanar circles that have the same center; Diameter-a
segment that contains the center of a circle and has its endpoints on the circle; Major arc-an arc that
measures greater than 180 degrees but less than 360 degrees; Minor arc-an arc that measures greater
than zero degrees but less than 180 degrees; Radius-a segment from the center of a circle to a point on
the circle; Sector of a circle-a region bounded by an arc of the circle and the two radii to the arc’s
endpoints; Segment of a circle-a part of a circle bounded by an arc and the segment joining its
endpoints.
Mathematics: Geometry
Content: Surface Area and Volume
v. 2015 - 2016
Duration: May (3 weeks)
Essential How do you find the surface area and volume of a solid and how do the surface areas and volumes of
Question: similar solids compare?
Skill:
Assessment:
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Recognize polyhedral and their parts.
Visualize cross sections of space figures.
Find the surface area of a prism, a cylinder, a pyramid, and a cone.
Find the volume of a prism, a cylinder, a cone, and a pyramid.
Find the surface area and volume of a sphere.
Compare and find the areas and volumes of similar solids.
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What is the number of edges in a pyramid with seven faces?
Describe the cross section formed in each diagram.
Find the surface area and volume of each:
Sphere with radius 4 feet, square pyramid with slant height 9 in and base 8 in, cylinder with radius 3
cm and height 8 cm
Resources: Pearson Geometry Common Core: Chapter 11, pages 688-755
CC.2.3.HS.A.8-Apply geometric theorems to verify properties of circles.
CC.2.3.HS.A.13-Analyze relationships between two-dimensional and three-dimensional objects.
CC.2.3.HS.A.9-Extend the concept of similarity to determine arc lengths and areas of sectors of circles.
CC.2.3.8.A.1-Apply the concepts of volume of cylinders, cones, and spheres to solve real-world and
mathematical problems.
CC.2.3.HS.A.12-Explain volume formulas and use them to solve problems.
Standards:
G.1.1.1.1-Identify, determine, and/or use the radius, diameter, segment, and/or tangent of a circle.
G.1.1.1.2-Identify, determine, and/or use the arcs, semicircles, sectors, and/or angles of a circle.
G.1.1.1.4-Identify and/or use the properties of a sphere or cylinder.
G.1.1.1-Identify and/or use parts of circles and segments associated with circles, spheres, and cylinders.
G.1.2.1.5-Identify and/or use properties of pyramids and prisms.
G.2.2.2-Use and/or develop procedures to determine or describe measures of perimeter, circumference,
and/or area.
G.2.3.1.1-Calculate the surface area of prisms, cylinders, cones, pyramids, and/or spheres.
G.2.3.1.2-Calculate the volume of prisms, cylinders, cones, pyramids, and/or spheres.
G.2.3.1.3-Find the measurement of a missing length given the surface area or volume.
G.2.3.1-Use and/or develop procedures to determine or describe measures of surface area and/or
volume.
G.2.3.2.1-Describe how a change in the linear dimension of a figure affects its surface area or volume.
G.2.3.2-Describe how a change in one dimension of a three-dimensional figure affects other
measurements of that figure.
Mathematics: Geometry
Vocabulary:
Comments:
v. 2015 - 2016
Cross section-is the intersection of a solid and a plane; Cylinder-a solid that has two congruent parallel
bases that are circles; Edge-is a segment that is formed by the intersection of two faces; Polyhedron-is
a space figure whose surfaces are polygons; Prism-a polyhedron with two congruent parallel faces, called
bases; Pyramid-is a polyhedron in which one face (the base) can be any polygon and the other faces are
triangles that meet at a common vertex; Surface area-the sum of the area of all the surfaces of a 3
dimensional figure; Volume-is the space that a figure occupies.
Mathematics: Geometry
Content: Circles
v. 2015 - 2016
Duration: May/ June (3 weeks)
Essential How do you find the equation of a circle in the coordinate plane and how can you prove relationships
Question: between angles and arcs in a circle?
Skill:
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Use properties of a tangent to a circle.
Use congruent chords, arcs, and central angles.
Use perpendicular bisectors to chords.
Find the measure of an inscribed angle.
Find the measure of an angle formed by a tangent and a chord.
Find measures of angles formed by chords, secants, and tangents.
Find the lengths of segments associated with circles.
Write the equation of a circle.
Find the center and radius of a circle.
Draw and describe a locus.
Assessment:
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Graph: (𝑥 + 3)2 + (𝑦 − 2)2 = 9
Write an equation of the circle with center (3, 0) that passes through point (-2, -4).
Write an equation for the locus of points in the coordinate plane that are 4 units from (-5, 2).
What is the difference between a tangent and secant of a circle?
Resources: Pearson Geometry Common Core: Chapter 12, pages 762-817
CC.2.3.HS.A.8-Apply geometric theorems to verify properties of circles.
G.1.1.1.1-Identify, determine, and/or use the radius, diameter, segment, and/or tangent of a circle.
Standards: G.1.1.1.2-Identify, determine, and/or use the arcs, semicircles, sectors, and/or angles of a circle.
G.1.1.1.3-Use chords, tangents, and secants to find missing arc measures or missing segment measures.
G.1.1.1--Identify and/or use parts of circles and segments associated with circles, spheres, and cylinders.
Vocabulary:
Comments:
Chord-a segment with both of its endpoints on a circle; Inscribed angle-an angle whose vertex is on
the circle and whose sides are chords of the circle ; Point of tangency-the point where a tangent and a
circle intersect; Secant-is a line that intersects a circle at two points; Tangent to a circle-is a line in the
plane of a circle that intersects the circle in exactly one point.