Download Unit 2 Geometric Angle Theorems

Unit 2 Geometric Angle Theorems
In this unit you will learn:
 The relationship between pairs of angles formed by transversals and the angles in a triangle.
 How to find area and perimeter of triangles, parallelograms, and trapezoids.
 The relationship among the three sides of a right triangle
 How to estimate value of square roots
 How to determine when the lengths of three segments can and cannot form a triangle.
Planned Teaching Window: 9/24/12 - 10/5/12
Unit should be Tested by 10/12/11
Give multiple dips (quizzes) before Unit Assessment
Give Standard Retake if needed
Standards will be tested again on the Semester 1 Midterm & Final
2.1 Angle Relationships
I can correctly identify the relationship between pairs of angles formed by intersecting lines, both
parallel and perpendicular, pairs of lines. G.2.A, G.2.B, G.2.D
This means I can
 Identify complementary, supplementary, alternate interior/exterior, same-side
interior/exterior (co-interior/exterior), and corresponding angle pairs
 Calculate the measure of angles given one or two angles on a diagram using the angle
relationships identified above
 Know, prove and apply theorems about parallel and perpendicular lines.
CPM Materials:
2.1.1 - 2.1.3
Will need extra practice
State EOC Examples:
 Prove that a point on the perpendicular bisector of a line segment is equidistant from the ends of the
line segment.
 If each of two lines is perpendicular to a given line, what is the relationship between the two lines?
How do you know?
 Prove that if two parallel lines are cut by a transversal, then alternate interior angles are equal.
 Describe all the ways that three planes can intersect in space.
Find the measure of each angle in the diagram below. Name any relationship you use to help you find each
measure.
c
b e
150°
a
110° i
j f
140°
h
d
g
[ a = 30 (supp with 150) b = 40 (sum of ’s in  = 180)
c = 40 (supp with 140) d = 40 (corresponding with c) e =110 (alt. int to 110)
f = 110 (vertical to 110) g = 30 (sum of ’s in  = 180) h = 140 (supp with d)
i = 70 (supp with f) j = 70 vertical to i or supp to 110 or f) ]
4/29/2017 4:57 PM
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Unit 2 Outline
2.2 Triangle Angle Relationships
I can correctly identify the relationship between angles formed inside a triangle. G.3.A
This means I can
 Use the Triangle Angle Sum Theorem to find missing angles in a triangle
 Know and apply basic postulates and theorems about triangles and special lines, line
segments, and rays associated with triangles
CPM Materials:
2.1.4 - 2.1.5
2.3.2
Will need extra practice.
State EOC Examples:
 Prove that the sum of the angles of a triangle is 1800.
 Prove and explain theorems about the incenter, circumcenter, orthocenter, and centriod.
 The rural towns of Atwood, Bridgeville, and Carenegie are building a communications tower to
serve the needs of all three towns. They want to position the tower so that the distance from each
town to the tower is equal. Where should they locate the tower? How far will it be from each town?
Find the value of x in the triangle below.
x
31
Find the maximum and minimum values for x.
x
8
[ 25 and 9 ]
17
4/29/2017 4:57 PM
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Unit 2 Outline