Download Geometry Course Summary Department: Math Semester 1 Learning

Geometry Course Summary
Department: Math
Semester 1
Learning Objective #1
Geometry Basics
Targets to Meet Learning Objective #1
 Use inductive reasoning to make conclusions about mathematical patterns
 Give the appropriate notation for line, segment, ray, and angle.
 Draw representations of given geometric situations
 Determine whether points are collinear or coplanar
 Determine the distance or length of any segment given the coordinates of its endpoints
 Use the segment addition postulate to determine the length of segments that are separated
into two or more segments
 Classify angles into groups according to the measure of their angles
 Use angle addition postulate to determine the measure of angles that are separated into two or
more angles
 Use the midpoint formula to find the midpoint between two given endpoints
 Find one endpoint given the other endpoint and the midpoint
 Tell the difference between intersect and bisect
 Identify vertical angles and linear pairs.
 Find missing measurements using the fact that vertical angles are equal and linear pairs = 180
 Find missing measures using the ideas of complementary and supplementary
 Find perimeter of any basic figure
 Use area formulas for triangle, rectangle, square, and circle
 Find a missing measurement given the area
Timeline
8 blocks
Learning Objective #2
Geometric Thinking
Targets to Meet Learning Objective #2
 Write conditional statements in if-then form
 Label parts of conditional statement
 Write converse, inverse, and contrapositive
 Write biconditional statements if the properties for a biconditional statement exist
 Use law of detachment and syllogism to make conjectures from other statements
 Use inductive and deductive reasoning to make conjectures about given information
 Use the algebraic properties of equality to solve equations and give a proof
 Write a two-column proof for segment theorems
 Write a two-column proof for angle theorems
Timeline
7 blocks
Learning Objective #3
Parallel and Perpendicular Lines
Targets to Meet Learning Objective #3
 Parallel lines, parallel planes, skew lines, and perpendicular lines
 Identify special angles formed by a transversal
 Use angle relationship postulates to solve for missing measurements in pictures of parallel lines
cut by a transversal.
 Prove that two angles are either congruent or supplementary using angle relationship postulates
 Prove that two lines are parallel by using angle relationship postulates
 Identify properties that exist when multiple lines are parallel or perpendicular and use those
properties to design a city of their own.
 Write the equation of a line given a variety of information
 Write the equation of a line that is parallel to another and goes through a given point
 Write the equation of a line that is perpendicular to another and goes through a given point
Timeline
8 blocks
Learning Objective #4
Triangle Congruence
Targets to Meet Learning Objective #4
 Classify triangles according to the angle measures and side lengths.
 Define basic parts of triangles
 Find the third angle in a triangle
 Use the exterior angle theorem to find missing measurements
 Recognize congruent triangles by identifying corresponding parts
 Use congruence of figures to find missing measurements
 Use given information to recognize which congruence postulate could be used to prove that two
triangles are congruent
 Use congruence postulates to write two column proofs for congruent triangles
 Understand that proving two triangles are congruent can also lead to proving that other
corresponding pieces must also be congruent (CPCTC)
 Know the parts of an isosceles triangle
 Understand the relationship between base angles and legs in an isosceles triangle
 Use the hypotenuse-leg congruence theorem to write a two column proof for congruent
triangles
Timeline
8 blocks
Semester 2
Learning Objective #5
Special Triangle Segments and Transformations
Targets to Meet Learning Objective #5
 Use the properties of perpendicular bisectors and angle bisectors in a triangle
 Identify medians and altitudes of a triangle
 Use the midsegment of a triangle to solve for missing lengths
 Use triangle inequalities to describe properties of the third side of a triangle.
 Describe rigid transformations in a coordinate plane as a translation, reflection, or rotation
 Identify, use, and algebraically describe reflections in the coordinate plane
 Students will be able to identify, use, and algebraically describe translations and rotations in the
coordinate plane
Timeline
4 blocks
Learning Objective #6
Quadrilaterals
Targets to Meet Learning Objective #6
 Classify polygons according to number of sides and special properties
 Use the sum of quadrilaterals to find missing angle measurements in a quadrilateral
 Use special properties of parallelograms to find missing measurements in a parallelogram.
 Prove that a quadrilateral is a parallelogram by identifying special properties of a parallelogram
 Find values within a quadrilateral that would make the figure be a parallelogram
 Use properties of special parallelograms to find missing measurements in a figure.
 Compare and contrast different types of parallelograms
 Use properties of trapezoids and kites to find missing measurements.
 Use area formulas for quadrilaterals
Timeline
7 blocks
Learning Objective #7
Similarity
Targets to Meet Learning Objective #7
 Student should be able to reduce ratios of the same unit or different units
 Student should be able to solve proportions
 Given a true proportion, students should be able to analyze new proportions and verify their
validity
 Student should be able to determine whether two figures meet the properties of similarity
 Student should be able to find missing measurements in two similar figures using proportions
 Students should be able to determine whether two figures are similar by any of the three
similarity postulates ( AA similarity, SSS Similarity, SAS Similarity)
Timeline
6 blocks
Learning Objective #8
Trigonometry and the Unit Circle
Targets to Meet Learning Objective #8
 Use the Pythagorean theorem to find missing pieces in a right triangle
 Use the Pythagorean theorem to help classify a triangle
 Discuss angle measures in terms of degrees or radians
 Convert between radians/degrees
 Fill in the unit circle for angle measures in both degrees and radians
 Find missing lengths in a 30-60-90 triangle
 Find the missing lengths in a 45-45-90 triangle.
 Use the 30-60-90 and 45-45-90 relationships to fill in the points on the unit circle
 Set up all trigonometric ratios for a right triangle
 Use a calculator to find trigonometric values for angles measured in degrees
 Use trigonometric ratios to find missing side lengths of a right triangle
 Use trigonometric ratios to find missing angle measures of a right triangle
Timeline
8 blocks
Learning Objective #9
Circles
Targets to Meet Learning Objective #9
 Identify segments and lines related to circles.
 Use the arc addition postulate to find missing arc mesurments
 Use properties involving congruent chord/arcs to find missing measurements
 Use inscribed angles of any kind to find missing arc measures
 Write the equation of a circle given the radius and center
 Graph a circle from the equation
Timeline
4 blocks
Learning Objective #10
Polygons and Sectors
Targets to Meet Learning Objective #10
 Find the surface area of a prism, cylinder, pyramid, or cone
 Find the volume of prisms, cylinders, pyramids, and cones
 Find the surface area and volume of a sphere
 Find and use the scale factor of similar solids
Timeline
5 blocks
Learning Objective #11
3 Dimensional Figures
Targets to Meet Learning Objective #11
 Find the surface area of a prism, cylinder, pyramid, or cone
 Find the volume of prisms, cylinders, pyramids, and cones
 Find the surface area and volume of a sphere
 Find and use the scale factor of similar solids
Timeline
4 blocks