Pulling a One-Eighty! - Kyrene School District

Lesson 10.1 Assignment

Name_________________________________________________________ Date__________________________

Pulling a One-Eighty!

Triangle Sum, Exterior Angle, and Exterior Angle Inequality Theorems

1. Use the figure shown to answer the questions.

P 21?

62? U

35? B M

a. Explain how you can use the Exterior Angle Theorem to calculate the measure of /PMU. The Exterior Angle Theorem states that the measure of the exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles of the triangle. Angle PMU is an exterior angle to nPBM and its corresponding remote interior angles are /PBM and /BPM. So, I can calculate the sum of those two angle measures to find the measure of /PMU.

b. Calculate the measure of /PMU. Show your work. m/PMU 5 m/PBM 1 m/BPM 5 35? 1 21? 5 56? The measure of /PMU is 56?.

? 2011 Carnegie Learning

Chapter 10 Assignments ? 195

Lesson 10.1 Assignment

page 2

c. Explain how you can use the Triangle Sum Theorem to calculate the measure of /UPM. The Triangle Sum Theorem states that the sum of the measures of the interior angles of a triangle is 180?. I know that the sum of the three angles in nUPM must equal 180?. I can add the measures of /PUM and /PMU and then subtract that total from 180? to find the measure of /UPM.

d. Calculate the measure of /UPM. Show your work. m/PMU 1 m/MUP 1 m/UPM 5 180? 56? 1 62? 1 m/UPM 5 180? 5 62? The measure of /UPM is 62?.

e. Which side of nPUB is the longest? Explain your reasoning. The measure of /UPB is 62? 1 21? or 83?, which makes it the largest angle in the triangle.

___

So, U Bis the longest side because it is across from the largest angle.

f. Which side of nPUB is the shortest? Explain your reasoning. Side PU is the shortest side because it is across from the smallest angle.

g. List the sides of nPMB in order from shortest to longest. Explain how you determined your answer.

____ ____ ___

MB, P M, P B Side MB is across from the smallest angle, which makes it the shortest side. Side PB is across from the largest angle, which makes it the longest side.

? 2011 Carnegie Learning

196 ? Chapter 10 Assignments

Lesson 10.2 Assignment

Name_________________________________________________________ Date__________________________

Triangle Construction I

Constructing Triangles

In each exercise, do the following: a.Use the given information to construct a triangle. b.Determine whether it is possible to use the given information to construct another triangle that is not congruent to the first triangle. c.If it is possible to construct another triangle that is not congruent to the first triangle, construct it. If it is not possible, explain why not.

1. Use the two line segments and the included angle to construct nXYZ.

X

Y

Y

Z

Y

a.

Z

X

Y

b. It is not possible to construct another triangle that is not congruent to the first triangle.

c. It is not possible because two segments and an included angle determine a unique triangle.

? 2011 Carnegie Learning

Chapter 10 Assignments ? 197

Lesson 10.2 Assignment

2. Use the three angles to construct nJ KL.

page 2

J

K

L

a.

K

J

L

b. It is possible to construct another triangle that is not congruent to the first triangle. c. Triangle JKL below has the same angle measures as triangle JKL, but the lengths of the

sides are different.

K

J

L

? 2011 Carnegie Learning

198 ? Chapter 10 Assignments

Lesson 10.2 Assignment

page 3

Name_________________________________________________________ Date__________________________

3. Use the two angles and the included side to construct nMNP.

N

M

M

N

a.

P

M

N

b. It is not possible to construct another triangle that is not congruent to the first triangle. c. It is not possible because two angles and an included side determine a unique triangle.

? 2011 Carnegie Learning

Chapter 10 Assignments ? 199

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download