Warm Up 1. What are two angles whose sum is 90°? 2. What are two angles whose sum is 180°?

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Warm Up 1. What are two angles whose sum is 90°? 2. What are two angles whose sum is 180°?

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Warm Up 1. What are two angles whose sum is 90°? 2. What are two angles whose sum is 180°?

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Warm Up

1. What are two angles whose sum is 90°?

2. What are two angles whose sum is 180°?

3. A part of a line between two points is called a _________.

4. Two lines that intersect at 90° are ______________.

complementary angles

supplementary angles

segment

perpendicular

Learn to classify triangles and solve problems involving angle and side measures of triangles.

Vocabulary

acute triangle

obtuse triangle

right triangle

congruent line segments

scalene triangle

isosceles triangle

equilateral triangle

A triangle is a closed figure with three line segments and three angles. Triangles can be classified by the measures of their angles. An acute triangle has only acute angles. An obtuse triangle has one obtuse angle. A right triangle has one right angle.

To decide whether a triangle is acute, obtuse, or right, you need to know the measures of its angles.

The sum of the measures of the angles in any triangle is 180°. You can see this if you tear the corners from a triangle and arrange them around a point on a line.

By knowing the sum of the measures of the angles in a triangle, you can find unknown angle measures.

To classify the triangle, find the measure of D on the trophy.

m D = 180° – (38° + 52°)

m D = 180° – 90°

m D = 90°

Additional Example 1: Application

Sara designed this triangular trophy. The measure of E is 38°, and the measure of F is 52°. Classify the triangle.

E

D

F

Subtract the sum of the known angle measures from 180°

So the measure of D is 90°. Because DEF has one right angle, the trophy is a right triangle.

To classify the triangle, find the measure of D on the trophy.

m D = 180° – (22° + 22°)

m D = 180° – 44°

m D = 136°

Check It Out: Example 1

E

Sara designed this triangular trophy. The measure of E is 22°, and the measure of F is 22°. Classify the triangle.

D

F

Subtract the sum of the known angle measures from 180°

So the measure of D is 136°. Because DEF has one obtuse angle, the trophy is an obtuse triangle.

You can use what you know about vertical, adjacent, complementary, and supplementary angles to find the measures of missing angles.

Q

P

T

68°

55°

S

R

Additional Example 2A: Using Properties of Angles to Label Triangles

Use the diagram to find the measure of each indicated angle.

QTR

QTR and STR are supplementary angles, so the sum of mQTR andmSTR is 180°.

mQTR = 180° – 68°

= 112°

Q

P

T

m SRT = 180° – (68° + 55°)

68°

55°

S

R

m QRT = 90° – 57°

Additional Example 2B: Using Properties of Angles to Label Triangles

QRT

QRT and SRT are complementary angles, so the sum of mQRT andmSRT is 90°.

= 180° – 123°

= 57°

= 33°

M

L

N

44°

60°

m MNO = 180° – 44°

P

O

Check It Out: Example 2A

Use the diagram to find the measure of each indicated angle.

MNO

MNO and PNO are supplementary angles, so the sum of mMNO andmPNO is 180°.

= 136°

MON and PON are complementary angles, so the sum of m MON andm PON is 90°.

M

L

N

m PON = 180° – (44° + 60°)

44°

60°

P

O

m MON = 90° – 76°

Check It Out: Example 2B

MON

= 180° – 104°

= 76°

= 14°

Congruent line segments have the same length. Triangles can be classified by the lengths of their sides. A scalene triangle has no congruent sides. An isosceles triangle has at least two congruent sides. An equilateral triangle has three congruent sides.

Additional Example 3: Classifying Triangles by Lengths of Sides

Classify the triangle. The sum of the lengths of the sides is 19.5 in.

M

c + (6.5 + 6.5) = 19.5

6.5 in.

6.5 in.

c + 13 = 19.5

c + 13 –13= 19.5 – 13

L

N

c = 6.5

c

Side c is 6.5 inches long. Because LMN has three congruent sides, it is an equilateral triangle.

Side d is 2.2 inches long. Because ABC has two congruent sides, it is an isosceles triangle.

Check It Out: Example 3

Classify the triangle. The sum of the lengths of the sides is 15.6 in.

B

d + (7.2 + 7.2) = 16.6

7.2 in.

7.2 in.

d + 14.4 = 16.6

d + 14.4 –14.4= 16.6 – 14.4

C

A

d = 2.2

d

Lesson Quiz

If the angles can form a triangle, classify the triangle as acute, obtuse, or right.

1. 37°, 53°, 90° 2. 65°, 110°, 25°

3. 61°, 78°, 41°4. 115°, 25°, 40°

The lengths of three sides of a triangle are given. Classify the triangle.

5. 12, 16, 256. 10, 10, 15

not a triangle

right

acute

obtuse

scalene

isosceles