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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

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

Classify triangles by their angle measures and side lengths.

Use triangle classification to find angle measures and side lengths.


Vocabulary

acute triangle

equiangular triangle

right triangle

obtuse triangle

equilateral triangle

isosceles triangle

scalene triangle


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.


C

A

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

B

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


By Angle Measures

Acute Triangle

Three acute angles


By Angle Measures

Equiangular Triangle

Three congruent acute angles


By Angle Measures

Right Triangle

One right angle


By Angle Measures

Obtuse Triangle

One obtuse angle


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.


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.


Example 1 - 3

Classify EHG, EFH, FHG by its angle measure

Triangle EHG is right

Triangle EFH is obtuse

Triangle FHG is equiangular


By Side Lengths

Equilateral Triangle

Three congruent sides


By Side Lengths

Isosceles Triangle

At least two congruent sides


By Side Lengths

Scalene Triangle

No congruent sides


Remember!

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


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

Class Example: Classifying Triangles by Side Lengths

Classify EHF by its side lengths.


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.


Example # 1 - 3

Classify ABC, ABD and ACD by its side lengths.

ABC = equilateral Triangle ABD = Scalene

Triangle ACD = scalene


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


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


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


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


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


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.


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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