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Geometry A Common Core Curriculum

Ron Larson, Laurie Boswell

Chapter 5

Congruent Triangles

Educators


Problem 1

WRITING Can a right triangle also be obtuse? Explain your reasoning.

Ali S.
Numerade Educator

Problem 2

COMPLETE THE SENTENCE The of an exterior angle of a triangle is equal to the sum of the measures of the two _____ interior angles.

Sally S.
Numerade Educator

Problem 3

In Exercises $3-6,$ classify the triangle by its sides and by measuring its angles.

Ali S.
Numerade Educator

Problem 4

In Exercises $3-6,$ classify the triangle by its sides and by measuring its angles.

Luca A.
Numerade Educator

Problem 5

In Exercises $3-6,$ classify the triangle by its sides and by measuring its angles.

Ali S.
Numerade Educator

Problem 6

In Exercises $3-6,$ classify the triangle by its sides and by measuring its angles.

Luca A.
Numerade Educator

Problem 7

In Exercises $7-10$ , classify $\triangle \mathrm{ABC}$ by its sides. Then determine whether it is a right triangle.
$$
\mathrm{A}(2,3), \mathrm{B}(6,3), \mathrm{C}(2,7)
$$

Ali S.
Numerade Educator

Problem 8

In Exercises $7-10$ , classify $\triangle \mathrm{ABC}$ by its sides. Then determine whether it is a right triangle.
$$
\mathrm{A}(3,3), \mathrm{B}(6,9), \mathrm{C}(6,-3)
$$

Luca A.
Numerade Educator

Problem 9

In Exercises $7-10$ , classify $\triangle \mathrm{ABC}$ by its sides. Then determine whether it is a right triangle.
$$
\mathrm{A}(1,9), \mathrm{B}(4,8), \mathrm{C}(2,5)
$$

Ali S.
Numerade Educator

Problem 10

In Exercises $7-10$ , classify $\triangle \mathrm{ABC}$ by its sides. Then determine whether it is a right triangle.
$$
\mathrm{A}(-2,3), \mathrm{B}(0,-3), \mathrm{C}(3,-2)
$$

Luca A.
Numerade Educator

Problem 11

In Exercises $11-14, $ $\mathrm{m} \angle 1 .$ Then classify the triangle by its angles.

Ali S.
Numerade Educator

Problem 12

In Exercises $11-14, $ $\mathrm{m} \angle 1 .$ Then classify the triangle by its angles.

Sally S.
Numerade Educator

Problem 13

In Exercises $11-14, $ $\mathrm{m} \angle 1 .$ Then classify the triangle by its angles.

Ali S.
Numerade Educator

Problem 14

In Exercises $11-14, $ $\mathrm{m} \angle 1 .$ Then classify the triangle by its angles.

Sally S.
Numerade Educator

Problem 15

In Exercises $15-18,$ nd the measure of the exterior angle.

Ali S.
Numerade Educator

Problem 16

In Exercises $15-18,$ nd the measure of the exterior angle.

Sally S.
Numerade Educator

Problem 17

In Exercises $15-18,$ nd the measure of the exterior angle.

Ali S.
Numerade Educator

Problem 18

In Exercises $15-18,$ nd the measure of the exterior angle.

Sally S.
Numerade Educator

Problem 19

In Exercises $19-22,$ I nd the measure of each acute angle.

Ali S.
Numerade Educator

Problem 20

In Exercises $19-22,$ I nd the measure of each acute angle.

Luca A.
Numerade Educator

Problem 21

In Exercises $19-22,$ I nd the measure of each acute angle.

Ali S.
Numerade Educator

Problem 22

In Exercises $19-22,$ I nd the measure of each acute angle.

Luca A.
Numerade Educator

Problem 23

In Exercises $23-26,$ ind the measure of each acute angle in the right triangle.
The measure of one acute angle is 5 times the measure of the other acute angle.

Ali S.
Numerade Educator

Problem 24

In Exercises $23-26,$ ind the measure of each acute angle in the right triangle.
The measure of one acute angle is 8 times the measure of the other acute angle.

Luca A.
Numerade Educator

Problem 25

In Exercises $23-26,$ ind the measure of each acute angle in the right triangle.
The measure of one acute angle is 3 times the sum of the measure of the other acute angle and $8 .$

Ali S.
Numerade Educator

Problem 26

In Exercises $23-26,$ ind the measure of each acute angle in the right triangle.
The measure of one acute angle is twice the difference of the measure of the other acute angle and 12 .

Luca A.
Numerade Educator

Problem 27

ERROR ANALYSIS In Exercises 27 and $28,$ describe and correct the error in 1 ending $\mathrm{m} \angle 1$

Ali S.
Numerade Educator

Problem 28

ERROR ANALYSIS In Exercises 27 and $28,$ describe and correct the error in 1 ending $\mathrm{m} \angle 1$

Luca A.
Numerade Educator

Problem 29

In Exercises $29-36,$ and the measure of the numbered angle.
$$
\angle 1
$$

Ali S.
Numerade Educator

Problem 30

In Exercises $29-36,$ and the measure of the numbered angle.
$$
\angle 2
$$

Luca A.
Numerade Educator

Problem 31

In Exercises $29-36,$ and the measure of the numbered angle.
$$
\angle 3
$$

Ali S.
Numerade Educator

Problem 32

In Exercises $29-36,$ and the measure of the numbered angle.
$$
\angle 4
$$

Luca A.
Numerade Educator

Problem 33

In Exercises $29-36,$ and the measure of the numbered angle.
$$
\angle 5
$$

Ali S.
Numerade Educator

Problem 34

In Exercises $29-36,$ and the measure of the numbered angle.
$$
\angle 6
$$

Luca A.
Numerade Educator

Problem 35

In Exercises $29-36,$ and the measure of the numbered angle.
$$
\angle 7
$$

Ali S.
Numerade Educator

Problem 36

In Exercises $29-36,$ and the measure of the numbered angle.
$$
\angle 8
$$

Luca A.
Numerade Educator

Problem 37

USING TOOLS Three people are standing on a stage. The distances between the three people are shown in the diagram. Classify the triangle by its sides and by measuring its angles.

Ali S.
Numerade Educator

Problem 38

USING STRUCTURE Which of the following sets of angle measures could form a triangle? Select all
that apply.
A. $100^{\circ}, 50^{\circ}, 40^{\circ}$
B. $96^{\circ}, 74^{\circ}, 10^{\circ}$
C. $165^{\circ}, 113^{\circ}, 82^{\circ}$
D. $101^{\circ}, 41^{\circ}, 38^{\circ}$
E. $90^{\circ}, 45^{\circ}, 45^{\circ}$
F. $84^{\circ}, 62^{\circ}, 34^{\circ}$

Luca A.
Numerade Educator

Problem 39

MODELING WITH MATHEMATICS You are bending a strip of metal into an isosceles triangle for a sculpture. The strip of metal is 20 inches long. The $|$ first bend is made 6 inches from one end. Describe two ways you could complete the triangle.

Ali S.
Numerade Educator

Problem 40

THOUGHT PROVOKING Find and draw an object (or part of an object) that can be modeled by a triangle
and an exterior angle. Describe the relationship between the interior angles of the triangle and the
exterior angle in terms of the object.

Luca A.
Numerade Educator

Problem 41

PROVING A COROLLARY Prove the Corollary to the Triangle Sum Theorem (Corollary 5.1$)$ .
Given $\triangle A B C$ is a right triangle. Prove $\angle$ A and $\angle B$ are complementary.

Ali S.
Numerade Educator

Problem 42

PROVING A THEOREM Prove the Exterior Angle Theorem (Theorem 5.2$)$ .
Given $\triangle A B C$ , exterior $\angle B C D$ Prove $m \angle A+m \angle B=m \angle B C D$

Luca A.
Numerade Educator

Problem 43

CRITICAL THINKING Is it possible to draw an obtuse isosceles triangle? obtuse equilateral triangle?
If so, provide examples. If not, explain why it is not possible.

Ali S.
Numerade Educator

Problem 44

CRITICAL THINKING:Is it possible to draw a right isosceles triangle? right equilateral triangle?
If so, provide an example. If not, explain why it is not possible.

Luca A.
Numerade Educator

Problem 45

MATHEMATICAL CONNECTIONS ABC is isosceles, $\mathrm{AB}=\mathrm{x},$ and $\mathrm{BC}=2 \mathrm{x}-4 .$
a. Find two possible values for $\mathrm{x}$ when the perimeter of $\Delta \mathrm{ABCis} 32$
b. How many possible values are there for $x$ when the perimeter of $\Delta$ ABC is 12$?$

Ali S.
Numerade Educator

Problem 46

HOW DO YOU SEE IT In as many ways as possible, classify each triangle by its appearance.

Luca A.
Numerade Educator

Problem 47

ANALYZING RELATIONSHIPS Which of the following could represent the measures of an exterior angle and two interior angles of a triangle? Select all that apply.
A. $100^{\circ}, 62^{\circ}, 38^{\circ}$
B. $81^{\circ}, 57^{\circ}, 24^{\circ}$
C. $119^{\circ}, 68^{\circ}, 49^{\circ}$
D. $95^{\circ}, 85^{\circ}, 28^{\circ}$
E. $92^{\circ}, 78^{\circ}, 68^{\circ}$
F. $149^{\circ}, 101^{\circ}, 48^{\circ}$

Ali S.
Numerade Educator

Problem 48

MAKING AN ARGUMENT Your friend claims the measure of an exterior angle will always be
greater than the sum of the nonadjacent interior angle measures. Is your friend correct? Explain
your reasoning.

Luca A.
Numerade Educator

Problem 49

MATHEMATICAL CONNECTIONS Exercises $49-52,$ I nd the values of $\mathrm{x}$ and $\mathrm{y}$ .

Ali S.
Numerade Educator

Problem 50

MATHEMATICAL CONNECTIONS Exercises $49-52,$ I nd the values of $\mathrm{x}$ and $\mathrm{y}$ .

Luca A.
Numerade Educator

Problem 51

MATHEMATICAL CONNECTIONS Exercises $49-52,$ I nd the values of $\mathrm{x}$ and $\mathrm{y}$ .

Ali S.
Numerade Educator

Problem 52

MATHEMATICAL CONNECTIONS Exercises $49-52,$ I nd the values of $\mathrm{x}$ and $\mathrm{y}$ .

Luca A.
Numerade Educator

Problem 53

PROVING A THEOREM Use the diagram to write a proof of the Triangle Sum Theorem (Theorem 5.1$)$ .
Your proof should be different from the proof of the Triangle Sum Theorem shown in this lesson.

Ali S.
Numerade Educator

Problem 54

Use the diagram to 1 nd the measure of the segment or angle.
$$
\mathrm{m} \angle \mathrm{KHL}
$$

Check back soon!

Problem 55

Use the diagram to 1 nd the measure of the segment or angle.
$$
\mathrm{m} \angle \mathrm{ABC}
$$

Ali S.
Numerade Educator

Problem 56

Use the diagram to 1 nd the measure of the segment or angle.
$$
\mathrm{GH}
$$

Check back soon!

Problem 57

Use the diagram to 1 nd the measure of the segment or angle.
$$
\mathrm{BC}
$$

Ali S.
Numerade Educator