Download Advanced Geometry

Radnor High School
Course Syllabus
Created 6/21/2011
Advanced Geometry
0424
Credits: 1
Weighted: No
Length: Year
Format: Meets daily
Grades: 9, 10
Prerequisite: Advanced Algebra 1 or 8th grade Algebra 1
Overall Description of Course
This course is a concept-based approach to traditional Geometry designed to reinforce and extend
previous algebra skills while integrating new geometric concepts. Students in Advanced Geometry derive
and use formulas for perimeter, circumference, area, surface area, and volume of many types of figures
use the Pythagorean Theorem, use congruence and similarity in describing relationships between figures
and analyze geometric figures. Some computer lab work may be performed during the year. Throughout
the course, algebra skills will be reviewed and reinforced through the application of geometric concepts.
Advanced Geometry is a College Preparatory level which features moderate pacing and workload with
teacher guidance to assist in the mastery of the material. Students enrolled on this level should be seeking
to satisfy college requirements/expectations of mathematics course but not necessarily have an interest in
pursuing math related college majors.
MARKING PERIOD ONE
Common Core Standards
A-REI.3. Solve linear equations and inequalities in one variable, including equations with coefficients
represented by letters.
A-REI.4. Solve quadratic equations in one variable.
A-REI.7. Solve a simple system consisting of a linear equation and a quadratic equation in two variables
algebraically and graphically.
G.CO.1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on
the undefined notions of point, line, distance along a line, and distance around a circular arc.
G-CO.6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given
rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to
decide if they are congruent.
G-CO.7. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if
and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
G-CO.8. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of
congruence in terms of rigid motions.
G-CO.9. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a
transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are
congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the
segment’s endpoints.
G-CO.10. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to
180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle
is parallel to the third side and half the length; the medians of a triangle meet at a point.
Keystone Connections:
Student Objectives:
At the end of this quarter, student should be able to successfully complete the following skills:
 Sketch intersection of a line and a plane
 Use segment postulate and distance formula
 Classify angles
 Bisect a segment and an angle
 Identify vertical angles, linear pair, complementary and supplementary angles
 Find the perimeter, circumference and area of plane figures
 Recognize and analyze conditional statements and write their inverses, converses amd
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contrapositives
Recognize and use biconditional statements for definitions
Identify relationships between lines
Identify angles formed by coplanar lines intersected by a transversal
Use slopes to decide if lines are parallel or perpendicular
Write the equation of a line parallel or perpendicular to a given line
Classify triangles by their sides and angles
Find angle measures in triangles
Identify congruent figures and corresponding parts
Prove triangles are congruent using SSS, SAS, ASA, AAS and HL
Materials & Texts
TEXTS
Geometry; McDougal & Littell, 2001
Activities, Assignments, & Assessments
ACTIVITIES
Basics of Geometry
 Points, lines, and planes
 Segments and their measures
 Angles and their measures
 Segment bisectors and angle bisectors
 Angle pair relationships
 Introduction to perimeter, area, and circumference
 Conditional statements
 Biconditional statements
Perpendicular and Parallel Lines
 Lines and angles
 Parallel lines and transversals
 Prove lines are parallel
 Using properties of parallel lines
 Slope
 Write equations of lines
 Identify parallel and perpendicular lines
 Write equations of parallel and perpendicular lines
Congruent Triangles
 Classify triangles
 Find angle measures in triangles
 Identify congruent triangles
 Prove triangles are congruent: SSS and SAS
 Prove triangles are congruent: ASA and AAS
ASSIGNMENTS
Assignment sheets will be distributed periodically throughout the school year. Homework will be
assigned on a daily basis. Individual assignments for each chapter can be viewed on the Mathematics
Department page of Radnor High School’s web site.
ASSESSMENTS
Homework will be assigned on a daily basis. Grades will be based on homework checks, quizzes and
chapter tests.
Terminology
conjecture, inductive reasoning, counterexample, point, line, plane, collinear, coplanar, line segment,
endpoint, initial point, opposite rays, intersection, postulate, coordinate, distance, length, between,
distance formula, congruent segment, angle, sides of an angle, vertex of an angle, congruent angle,
measure of an angle, acute angle, obtuse angle, right angle, straight angle, adjacent angle, midpoint,
bisect, segment bisector, compass, midpoint formula, angle bisector, vertical angle, linear pair,
complementary angles, supplementary angles, conditional statement, if-then form, hypothesis, conclusion,
converse, negation, inverse, contrapositive, equivalent statements, perpendicular lines, biconditional
statement, parallel lines, skew lines, transversal, corresponding angles, alternate interior angles, alternate
exterior angles, consecutive interior angles, same side interior angles, equilateral triangle, isosceles
triangle, scalene triangle, right triangle, obtuse triangle, vertex of a triangle, adjacent sides of a triangle,
legs of right triangle, hypotenuse, legs of an isosceles triangle, base of an isosceles triangle, interior angle,
exterior angle, congruent, corresponding angles, corresponding sides, base angles, vertex angle
Media, Technology, Web Resources
Graphing and/or scientific calculator
Compass and straight edge
Classzone: http://www.classzone.com/books/geometry/index.cfm?state=PA
MARKING PERIOD TWO
Common Core Standards
G-CO.11. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite
angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are
parallelograms with congruent diagonals.
G-GPE.4. Use coordinates to prove simple geometric theorems algebraically.
G-GPE.5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric
problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given
point).
G-GPE.6. Find the point on a directed line segment between two given points that partitions the segment in a
given ratio.
G-GPE.7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using
the distance formula.
Keystone Connections:
Student Objectives:
At the end of this quarter, student should be able to successfully complete the following skills:
 Use properties of perpendicular bisector of segments and angle bisectors
 Use properties of medians, altitudes midsegment of triangles
 Compare the lengths of the sides or the measures of the angles of a triangle
 Identify, name and describe polygons
 Use the sum of the measures of the interior angles of a quadrilateral
 Use properties of parallelograms
 Prove that a quadrilateral is a parallelogram
 Use properties of rhombi, rectangles and squares including properties of diagonals
 Use properties of trapezoids and kites
 Identify special types of quadrilaterals based on limited information
 Find the area of rectangles, kites, parallelograms, squares, triangles, trapezoids and rhombi
Materials & Texts
TEXTS
Geometry; McDougal & Littell, 2001
Activities, Assignments, & Assessments
ACTIVITIES
Congruent Triangles
 Write 2-column proofs
 Isosceles, equilateral, and right triangles
Properties of Triangles
 Perpendiculars and Bisectors
 Medians and Altitudes
 Midsegment Theorem
 Inequalities in one triangle
Polygons
 Identify polygons
 Angle measures in polygons
 Properties of parallelograms
 Prove quadrilaterals are parallelograms
 Rhombuses, rectangles and squares
 Trapezoids and kites
 Use slope and the distance formula to identify a special quadrilateral
 Areas of triangles and quadrilaterals
ASSIGNMENTS
Assignment sheets will be distributed periodically throughout the school year. Homework will be
assigned on a daily basis. Individual assignments for each chapter can be viewed on the Mathematics
Department page of Radnor High School’s web site.
ASSESSMENTS
Homework will be assigned on a daily basis. Grades will be based on homework checks, quizzes and
chapter tests. A midterm exam will be given at the end of the second quarter.
Terminology
perpendicular bisector, concurrent lines, median of a triangle, centroid of a triangle, altitude of a triangle,
midsegment of a triangle, polygon, convex, concave, regular, diagonal, parallelogram, rhombus,
rectangle, square, trapezoid, isosceles trapezoid, midsegment of a trapezoid, kite
Media, Technology, Web Resources
Graphing and/or scientific calculator
Compass and straight edge
Classzone: http://www.classzone.com/books/geometry/index.cfm?state=PA
MARKING PERIOD THREE
Common Core Standards
G-SRT.2. Given two figures, use the definition of similarity in terms of similarity transformations to decide if
they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality
of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
G-SRT.3. Use the properties of similarity transformations to establish the AA criterion for two triangles to be
similar.
G-SRT.4. Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides
the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.GSRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in
geometric figures.
G-SRT.6. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle,
leading to definitions of trigonometric ratios for acute angles.
G-SRT.7. Explain and use the relationship between the sine and cosine of complementary angles.
G-SRT.8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Keystone Connections:
Student Objectives:
At the end of this quarter, student should be able to successfully complete the following skills:
 Write and simplify the ratio of two numbers
 Use proportion to solve problems
 Understand the properties of proportions
 Identify similar polygons and use properties of similar polygons
 Prove that two triangles are similar using AA, SSS or SAS similarity theorem
 Use similarity theorems to solve problems
 Use the Pythagorean theorem and its converse
 Use side lengths to classify triangle
 Find side lengths of special right triangles
 Find trigonometric ratios of an acute angle of a right triangle
 Solve a right triangle
Materials & Texts
TEXTS
Geometry; McDougal & Littell, 2001
Activities, Assignments, & Assessments
ACTIVITIES
Similarity
 Ratio and proportion
 Similar polygons
 Similar triangles
 Prove triangles are similar
 Use proportionality theorems to find segment length
Right Triangles and Trigonometry
 Simplify radicals
 The Pythagorean Theorem
 The converse of the Pythagorean Theorem
 Special right triangles
 Trigonometric ratios
 Solve right triangles
ASSIGNMENTS
Assignment sheets will be distributed periodically throughout the school year. Homework will be
assigned on a daily basis. Individual assignments for each chapter can be viewed on the Mathematics
Department page of Radnor High School’s web site.
ASSESSMENTS
Homework will be assigned on a daily basis. Grades will be based on homework checks, quizzes and
chapter tests.
Terminology
Ratio, proportion, extremes, means, similar polygons, scale factor, Pythagorean triple, special right
triangles, trigonometric ratio, sine, cosine, tangent
Media, Technology, Web Resources
Graphing and/or scientific calculator
Compass and straight edge
Classzone: http://www.classzone.com/books/geometry/index.cfm?state=PA
MARKING PERIOD FOUR
Common Core Standards
G-C.1. Prove that all circles are similar.
G-C.2. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship
between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the
radius of a circle is perpendicular to the tangent where the radius intersects the circle.
G-C.3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a
quadrilateral inscribed in a circle.
G-C.4. (+) Construct a tangent line from a point outside a given circle to the circle.
G-C.5. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the
radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the
area of a sector.
G-GPE.1. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete
the square to find the center and radius of a circle given by an equation.
G-GMD.1. Give an informal argument for the formulas for the circumference of a circle, area of a circle,
volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit
arguments.
G-GMD.2. (+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a
sphere and other solid figures.
G-GMD.3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Keystone Connections:
Student Objectives:
At the end of this quarter, student should be able to successfully complete the following skills:
 Identify segments and lines related to circles
 Use properties of tangents, arcs and chords of circles
 Use properties of inscribed angles and inscribed polygons of circles
 Find and graph the equations of circles
 Find the measures of interior and exterior angles of a polygon
 Find the area of a regular polygon
 Compare perimeters and areas of similar figures
 Find the circumference of a circle and the length of an arc
 Find the area of a circle and area of a sector
 Find the surface areas and volumes of prisms, cylinders, pyramids, cones and spheres
Materials & Texts
TEXTS
Geometry; McDougal & Littell, 2001
Activities, Assignments, & Assessments
ACTIVITIES
Circles
 Tangents to circles
 Arcs and chords
 Inscribed Angles
 Other angles formed by tangents, secants, & chords
 Equations of circles
 Circumference and arc length
Area of Polygons and Circles
 Areas of regular polygons
 Perimeters and areas of similar figures
 Areas of circles and sectors
Surface Area and Volume
 Identify types and parts of solids
 Surface area of prisms and cylinders
 Surface area of pyramids and cones
 Volumes of prisms and cylinders
 Volumes of pyramids and cones
 Surface area and volume of spheres
ASSIGNMENTS
Assignment sheets will be distributed periodically throughout the school year. Homework will be
assigned on a daily basis. Individual assignments for each chapter can be viewed on the Mathematics
Department page of Radnor High School’s web site.
ASSESSMENTS
Homework will be assigned on a daily basis. Grades will be based on homework checks, quizzes and
chapter tests. Final exam will be given at the end of the school year.
Terminology
circle, center of a circle, radius of a circle, diameter, chord, secant, tangent, tangent circles, concentric
circles, common tangent, point of tangency, central angle, minor arc, major arc, semicircle, inscribed
angle, intercepted arc, inscribed polygon, circumscribed circle, tangent segment, secant, center of a
polygon, radius of a polygon, apothem of a polygon, central angle of a regular polygon, circumference,
arc length, sector of a circle, lateral faces, right prism, surface area, lateral area, cylinder, pyramid, cone,
volume, sphere
Media, Technology, Web Resources
Graphing and/or scientific calculator
Compass and straight edge
Classzone: http://www.classzone.com/books/geometry/index.cfm?state=PA
Enduring Understandings
Essential Questions