6th Grade Math HomeworkCh. 7-5

Page 346#6-14 & #28-36

(Spiral Review)

Ch 7 Learning Goal: PLANE GEOMETRY• Learn to describe the figures by using the terms of geometry (7-1)• Learn to name, measure, classify, estimate and draw angles (7-2)• Learn to understand relationship of angles (7-3)• Learn to classify the different types of lines (7-4)• Learn to classify triangles and solve problems involving angle and side

measures of triangles (7-5)• Learn to identify, classify, and compare quadrilaterals (7-6)• Learn to identify regular and not regular polygons and to find the angle

measures of regular polygons (7-7)• Learn to recognize, describe, and extend geometric patterns (7-8)• Learn to identify congruent figures and to use congruence to solve

problems (7-9)• Learn to use translations, reflections, and rotations to transform geometric

shapes (7-10)• Learn to identify line symmetry (7-11)• Learn to identify tessellations and shapes that can tessellate (7-12)

7-5 Triangles

Course 1

Warm UpWarm Up

Lesson PresentationLesson PresentationProblem of the DayProblem of the Day

Warm Up1. 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

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7-5 Triangles

perpendicular

Problem of the DayFind the total number of shaded triangles in each figure.

3 6 10

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7-5 Triangles

Today’s Learning Goal AssignmentLearn to classify triangles and solve problems involving angle and side measures of triangles. Course 1

7-5 Triangles

Vocabularyacute triangleobtuse triangleright trianglescalene triangleisosceles triangleequilateral triangle

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Course 1

7-5 Triangles

Course 1

7-5 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.

Acute triangle Obtuse triangle Right triangle

Course 1

7-5 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.

Course 1

7-5 TrianglesAdditional 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.

Course 1

7-5 TrianglesTry This: Example 1

D

E

F

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°

m 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.

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7-5 Triangles

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

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7-5 TrianglesAdditional Example 2A: Using Properties of Angles

to Label TrianglesUse the diagram to find the measure of each indicated angle.

QTR and STR are supplementary angles, so the sum of m QTR and m STR is 180°.m QTR = 180° – 68°

= 112°

P

S R

Q

T

68°

55°

A. QTR

Course 1

7-5 TrianglesTry This: 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 m PNO is 180°.

m MNO = 180° – 44° = 136°

L

P O

M

N44°

60°

A. MNO

Course 1

7-5 TrianglesAdditional Example 2B: Using Properties of Angles

to Label Triangles

QRT and SRT are complementary angles, so the sum of m QRT and m SRT is 90°.m SRT = 180° – (68° + 55°) = 180° – 123°

= 57°m QRT = 90° – 57°

= 33°

P

S R

Q

T

68°

55°

B. QRT

Course 1

7-5 TrianglesTry This: 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

N44°

60°

B. MON

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7-5 Triangles

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.

Course 1

7-5 TrianglesAdditional Example 3: Classifying Triangles by

Lengths of SidesClassify 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 equilateral.

Course 1

7-5 TrianglesTry This: Example 3

Classify the triangle. The sum of the lengths of the sides is 21.6 in.

d = 7.2

7.2 in.

C A d

B

d + (7.2 + 7.2) = 21.6 d + 14.4 = 21.6 d + 14.4 – 14.4 = 21.6 – 14.4

7.2 in.

Side d is 7.2 inches long. Because ABC has three congruent sides, it is equilateral.

Lesson QuizIf 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

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acute obtuse

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7-5 Triangles

scalene isosceles