8-5 triangles warm up warm up lesson presentation lesson presentation problem of the day problem of...

8-5 Triangles

Warm UpWarm Up

Lesson Presentation

Problem of the Day

Lesson Quizzes

8-5 Triangles

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

8-5 Triangles

Problem of the Day

Find the total number of shaded triangles in each figure.

3 6 10

8-5 Triangles

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

8-5 Triangles

Vocabulary

acute triangleobtuse triangleright trianglecongruent line segmentsscalene triangleisosceles triangleequilateral triangle

8-5 Triangles

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.

8-5 Triangles

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.

8-5 Triangles

Additional Example 1: Application

D

E

F

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

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

Subtract the sum of the known angle measures from 180°

m D = 180° – (38° + 52°)

m D = 180° – 90°

m D = 90°

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

8-5 Triangles

Check It Out: Example 1

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

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

Subtract the sum of the known angle measures from 180°

D

E

Fm D = 180° – (22° + 22°)

m D = 180° – 44°

m D = 136°

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

8-5 Triangles

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

8-5 Triangles

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

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

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

mQTR = 180° – 68°

= 112°

P

S R

Q

T

68°

55°

QTR

8-5 Triangles

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

QRT and SRT are complementary angles, so the sum of mQRT and mSRT is 90°.m SRT = 180° – (68° + 55°)

= 180° – 123°= 57°

m QRT = 90° – 57°

= 33°

P

S R

Q

T

68°

55°

QRT

8-5 Triangles

Check It Out: Example 2A

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

MNO and PNO are supplementary angles, so the sum of m MNO and mPNO is 180°.

m MNO = 180° – 44°

= 136°

L

P O

M

N

44°

60°

MNO

8-5 Triangles

Check It Out: Example 2B

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

m PON = 180° – (44° + 60°)

= 180° – 104°= 76°

m MON = 90° – 76°

= 14°

L

P O

M

N

44°

60°

MON

8-5 Triangles

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.

8-5 Triangles

Additional Example 3: Classifying Triangles by Lengths of Sides

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

c = 6.5

6.5 in.

N L c

M

c + (6.5 + 6.5) = 19.5

c + 13 = 19.5

c + 13 – 13 = 19.5 – 13

6.5 in.

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

8-5 Triangles

Check It Out: Example 3

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

d = 2.2

7.2 in.

C A d

B

d + (7.2 + 7.2) = 16.6

d + 14.4 = 16.6 d + 14.4 – 14.4 = 16.6 – 14.4

7.2 in.

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

8-5 Triangles

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

8-5 Triangles

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, 25 6. 10, 10, 15

not a triangleright

Insert Lesson Title Here

acute obtuse

scalene isosceles

8-5 Triangles

1. If the following angles can form a triangle, classify the triangle as acute, obtuse, or right.45, 45, 90

A. acute

B. right

C. obtuse

D. not a triangle


8-5 Triangles


A. acute

B. right

C. obtuse

D. not a triangle


8-5 Triangles

5. The lengths of three sides of a triangle are given. Classify the triangle. 8, 10, 12

A. equilateral

B. isosceles

C. scalene

D. right


The lengths of three sides of a triangle are given. Classify the triangle. 8, 10, 12

8-5 Triangles

6. The lengths of three sides of a triangle are given. Classify the triangle. 12, 8, 12

A. equilateral

B. isosceles

C. scalene

D. right


The lengths of three sides of a triangle are given. Classify the triangle. 8, 10, 12

8-5 triangles warm up warm up lesson presentation lesson presentation problem of the day problem of...

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