Name _________________________________Period ___ Date ______________
Grade 8 Module 2 –
Lesson 13
ESSENTIAL QUESTION:
How can algebraic concepts be applied to geometry?
G5: Use informal arguments to establish facts about the angle sum and
exterior angles of a triangle.
A. INQUIRY LAB: SUM OF THE INTERIOR ANGLES OF A TRIANGLE
STEP 1: Using a pair of scissors, cut a triangle out of the bottom corner of the paper.
STEP 2: Inside the triangle label each of the three angles with a letter
STEP 3: Tear off the three angles of the triangle, being sure to tear the letter too.
C
A
B
STEP 4: Rearrange the torn pieces so that all three vertices (angles) meet at one point.
STEP 5: Sketch the arrangement you made below.
What do you notice about these three angles when they are all put together?
What about your partner? Did s/he get the same results?
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Name _________________________________Period ___ Date ______________
CONCLUSIONS: The sum of the measures of the three angles of a triangle always
equals_______ degrees, or a(n) _______________ angle. 𝑚∠1 + 𝑚∠2 + 𝑚∠3 = ________°
45°
90°
𝑚∠1
+ 𝑚∠2 + 𝑚∠3 = ________°
_________ + ________ + ________
= ________°
If one angle of a triangle measures 32 degrees, and another angle measures 107 degrees, then
show work to find the measure of the third angle. The name of this triangle by its angles is
__________, and by its sides is _________________.
In a right triangle, an acute angle measures 50 degrees. Show work to determine the measure
of the other acute angle.
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Name _________________________________Period ___ Date ______________
B. INQUIRY LAB: SUM OF THE EXTERIOR ANGLES OF A TRIANGLE
STEP 1: Record the measurements of angles A, B, and C on the diagram. Angle A = 43⁰,
Angle B = 42⁰, and Angle C = 95⁰.
STEP 2: Using each vertex angle ONCE, extend a ray out from each vertex.
(One of the three is drawn for you)
STEP 3: Once done drawing these rays, label the three new angles D, E, F.
(One of the three is done for you)
A
B
D
C
Angle D is known as
a REMOTE angle or
an exterior angle of
the triangle.
STEP 4: Record the measurements of angles D, E, and F
on the diagram. Angle D = 138⁰, Angle E = 85⁰, and Angle
F = 137⁰.
Let’s see if we can find a relationship among these angles. What do you notice?
If you know the measures of the interior angles, are there ways to determine the
measure of the exterior angles?
SUM OF THE EXTERIOR ANGLES OF A TRIANGLE
The measure of an exterior angle is equal to the
sum of its two REMOTE interior angles.
Angle F = angle _____ + angle _____
Angle D = angle _____ + angle _____
Angle E = angle _____ + angle _____
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Name _________________________________Period ___ Date ______________
---------------------------------------------------------------------------------------------------------------------------Find the value of angle X.
X
22
134
Find the value of angle X.
X
120
58
Find the value of angle X.
X
125
170
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Name _________________________________Period ___ Date ______________
1) In the diagram below, line 𝐴𝐵 is parallel to line 𝐶𝐷, i.e., 𝐿𝐴𝐵 ∥ 𝐿𝐶𝐷 . The measure of angle
∠𝐴𝐵𝐶 = 28°, and the measure of angle ∠𝐸𝐷𝐶 = 42°.
What is the measure of angle ∠𝐶𝐸𝐷? _________________
Explain why you are correct by presenting an informal argument that uses the angle sum of a
triangle and what you know about corresponding angles and alternate interior angles.
2) In the diagram below, line 𝐴𝐵 is parallel to line 𝐶𝐷, i.e., 𝐿𝐴𝐵 ∥ 𝐿𝐶𝐷 . The measure of angle
∠𝐴𝐵𝐸 = 38°, and the measure of angle ∠𝐸𝐷𝐶 = 16°.
What is the measure of angle ∠𝐵𝐸𝐷? _________________
Explain why you are correct by presenting an informal argument that uses the angle sum of
a triangle and what you know about corresponding angles and alternate interior angles.
[Hint: Find the measure of angle ∠𝐶𝐸𝐷 first, and then use that measure to find the measure of
angle ∠𝐵𝐸𝐷.]
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Name _________________________________Period ___ Date ______________
3) In the diagram below, line 𝐴𝐵 is parallel to line 𝐶𝐷, i.e., 𝐿𝐴𝐵 ∥ 𝐿𝐶𝐷 . The measure of angle
∠𝐴𝐵𝐸 = 56°, and the measure of angle ∠𝐸𝐷𝐶 = 22°. (Hint: Extend the segment 𝐵𝐸 so
that it intersects line 𝐶𝐷.)
What is the measure of angle ∠𝐵𝐸𝐷? _________________
Explain why you are correct by presenting an informal argument that uses the angle sum of
a triangle and what you know about corresponding angles and alternate interior angles.
[Hint: Extend the segment 𝐵𝐸 so that it intersects line 𝐶𝐷.]
4) What is the measure of ∠𝐴𝐶𝐵? _________________
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Name _________________________________Period ___ Date ______________
5) What is the measure of ∠𝐸𝐹𝐷? _________________
6) What is the measure of ∠𝐻𝐼𝐺? _____________
7) What is the measure of ∠𝐴𝐵𝐶? ______________
8) Triangle 𝐷𝐸𝐹 is a right triangle. What is the measure of ∠𝐸𝐹𝐷? _________________
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Name _________________________________Period ___ Date ______________
9) In the diagram below, lines 𝐿1 and 𝐿2 are parallel. Transversals 𝑟 and 𝑠 intersect both lines
at the points shown below.
What is the measure of ∠𝐽𝑀𝐾? __________________
Explain how you know you are correct.
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