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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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4 1

4-1

Classifying Triangles

Holt Geometry

Warm Up

Lesson Presentation

Lesson Quiz


4 1

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


4 1

Objectives

Classify triangles by their angle measures and side lengths.

Use triangle classification to find angle measures and side lengths.


4 1

Vocabulary

acute triangle

equiangular triangle

right triangle

obtuse triangle

equilateral triangle

isosceles triangle

scalene triangle


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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.


4 1

C

A

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

B

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


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By Angle Measures

Acute Triangle

Three acute angles


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By Angle Measures

Equiangular Triangle

Three congruent acute angles


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By Angle Measures

Right Triangle

One right angle


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By Angle Measures

Obtuse Triangle

One obtuse angle


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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.


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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.


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Example 1 - 3

Classify EHG, EFH, FHG by its angle measure

Triangle EHG is right

Triangle EFH is obtuse

Triangle FHG is equiangular


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By Side Lengths

Equilateral Triangle

Three congruent sides


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By Side Lengths

Isosceles Triangle

At least two congruent sides


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By Side Lengths

Scalene Triangle

No congruent sides


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Remember!

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


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

Class Example: Classifying Triangles by Side Lengths

Classify EHF by its side lengths.


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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.


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Example # 1 - 3

Classify ABC, ABD and ACD by its side lengths.

ABC = equilateral Triangle ABD = Scalene

Triangle ACD = scalene


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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


4 1

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


4 1

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


4 1

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


4 1

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


4 1

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.


4 1

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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