Download Geometry 4-2 Measuring Angles in Triangles A. Theorems 1

Geometry 4-2 Measuring Angles in Triangles
A. Theorems
1. Theorem 4-1 – _________________ – The sum of the measures of a triangle is
________.
Example 1: Find x in the triangle.
x
68°
33°
2. Theorem 4-2 – ___________________ – If two angles of one triangle are
___________ to two angles of a second triangle, then the 3rd angles of the
triangles are ____________.
3. Theorem 4-3 – ___________________ – The measure of an exterior angle of
a triangle is equal to the _______ of the measures of the two remote interior
angles.
B. Definitions
1. Exterior angle - ∠ BCD is an exterior angle
2. Remote interior angle - ∠ A and ∠ B are two remote interior angles.
B
A
C
D
C. Explanation of Exterior Angle Theorem
Imagine ∠ BCA = 70°, how big is ∠ BCD = ________
Now, take a look at ABC, what is going to be the sum of ∠ A and ∠ B? = ____
Example 2: Find the measure of each numbered angle.
65°
46°
82°
1
2
4
5
3
142°
1. A flow proof organizes a series of statements in logical order, starting with the
given statement. Each statement is written in a box with the reason verifying
the statement written below the box.
Example 3: Write a flow proof of the Exterior Angle Theorem
C
Given: ABC
Prove: m ∠ CBD = m ∠ A + m ∠ C
D
Flow Proof:
B
A
∠ CBD and ∠ ABC form a linear pair.
ABC
Definition of a ________________
Given
∠ CBD and ∠ ABC are supplementary.
If 2 ∠ ’s form a ________________
m ∠ A + m ∠ ABC + m ∠ C = 180
m ∠ CBD + m ∠ ABC = 180
Definition of a ________________
m ∠ A + m ∠ ABC + m ∠ C = m ∠ CBD + m ∠ ABC
∠
m ∠ A + m ∠ C = m ∠ CBD
2. A statement that can be easily proved using a theorem
is called a __________.
a) Corollary 4.1 – The acute angles of a right triangle
are complimentary.
Example: m ∠ A + m ∠ C = __________
b) Corollary 4.2 – There can be at most one right or
obtuse angle in a triangle.
HW: Geometry 4-2 p.189-191
12-34 even, 36-39, 45, 47-48, 49-63 odd
A
B
C