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4-1. Classifying Triangles. Holt Geometry. Warm Up. Lesson Presentation. Lesson Quiz. Warm Up Classify each angle as acute, obtuse, or right. 1. 2. 3. 4. If the perimeter is 47, find x and the lengths of the three sides. right. acute. obtuse. x = 5; 8; 16; 23. Objectives.

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Presentation Transcript
slide1

4-1

Classifying Triangles

Holt Geometry

Warm Up

Lesson Presentation

Lesson Quiz

slide2

Warm Up

Classify each angle as acute, obtuse, or right.

1.2.

3.

4. If the perimeter is 47, find x and the lengths of the three sides.

right

acute

obtuse

x = 5; 8; 16; 23

slide3

Objectives

Classify triangles by their angle measures and side lengths.

Use triangle classification to find angle measures and side lengths.

slide4

Vocabulary

acute triangle

equiangular triangle

right triangle

obtuse triangle

equilateral triangle

isosceles triangle

scalene triangle

slide5

Recall that a triangle ( ) is a polygon with three sides. Triangles can be classified in two ways: by their angle measures or by their side lengths.

slide6

C

A

AB, BC, and AC are the sides of ABC.

B

A, B, C are the triangle\'s vertices.

slide7

By Angle Measures

Acute Triangle

Three acute angles

slide8

By Angle Measures

Equiangular Triangle

Three congruent acute angles

slide9

By Angle Measures

Right Triangle

One right angle

slide10

By Angle Measures

Obtuse Triangle

One obtuse angle

slide11

B is an obtuse angle. So BDC is an obtuse triangle.

Class Example: Classifying Triangles by Angle Measures

Classify BDC by its angle measures.

B is an obtuse angle.

slide12

Therefore mABD + mCBD = 180°. By substitution, mABD + 100°= 180°. SomABD = 80°. ABD is an acute triangle by definition.

Class Example: Classifying Triangles by Angle Measures

Classify ABD by its angle measures.

ABD andCBD form a linear pair, so they are supplementary.

slide13

Example 1 - 3

Classify EHG, EFH, FHG by its angle measure

Triangle EHG is right

Triangle EFH is obtuse

Triangle FHG is equiangular

slide14

By Side Lengths

Equilateral Triangle

Three congruent sides

slide15

By Side Lengths

Isosceles Triangle

At least two congruent sides

slide16

By Side Lengths

Scalene Triangle

No congruent sides

slide17

Remember!

When you look at a figure, you cannot assume segments are congruent based on appearance. They must be marked as congruent.

slide18

From the figure, . So HF = 10, and EHF is isosceles.

Class Example: Classifying Triangles by Side Lengths

Classify EHF by its side lengths.

slide19

By the Segment Addition Postulate, EG = EF + FG = 10 + 4 = 14. Since no sides are congruent, EHG is scalene.

Class Example: Classifying Triangles by Side Lengths

Classify EHGby its side lengths.

slide20

Example # 1 - 3

Classify ABC, ABD and ACD by its side lengths.

ABC = equilateral Triangle ABD = Scalene

Triangle ACD = scalene

slide21

Example # 1: Using Triangle Classification

Find the side lengths of JKL.

Step 1 Find the value of x.

JK = KL

4x – 1.3 = x + 3.2

3x = 4.5

x = 1.5

slide22

Example #1 Continued

Find the side lengths of JKL.

Step 2 Substitute 1.5 into the expressions to find the side lengths.

JK = 4x – 1.3

= 4(1.5) – 1.3 = 4.7

KL = x + 3.2

= 1(1.5) + 3.2 = 4.7

JL = 5x + 0.2

= 5(1.5) +0.2 = 7.3

slide23

Example # 2

Find the side lengths of equilateral FGH.

Step 1 Find the value of y.

Given.

FG = GH = FH

Def. of  segs.

Substitute

(3y – 4) for FG and (2y + 3) for GH.

3y – 4 = 2y + 3

Add 4 and subtract 2y from both sides.

y = 7

slide24

Check It Out! Example #2 Continued

Find the side lengths of equilateral FGH.

Step 2 Substitute 7 into the expressions to find the side lengths.

FG = 3y – 4

= 3(7) – 4 = 17

GH = 2y + 3

= 2(7) + 3 = 17

FH = 5y – 18

= 5(7) – 18 = 17

homework

Homework:

Page 219: # 1-19

slide26

Exit Question

Classify each triangle by its angles and sides.

1. MNQ

2.NQP

3. MNP

4. Find the side lengths of the triangle.

acute; equilateral

obtuse; scalene

acute; scalene

29; 29; 23

slide27

Exit Question Name:

Classify each triangle by its angles and sides.

1. MNQ

2.NQP

3. MNP

4. Find the side lengths of the triangle.

slide28

Exit Question Name:

Classify each triangle by its angles and sides.

1. MNQ

2.NQP

3. MNP

4. Find the side lengths of the triangle.

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