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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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Classifying Triangles

Holt Geometry

Warm Up

Lesson Presentation

Lesson Quiz

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

Classify triangles by their angle measures and side lengths.

Use triangle classification to find angle measures and side lengths.

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.

A

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

B

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

Acute Triangle

Three acute angles

Equiangular Triangle

Three congruent acute angles

Right Triangle

One right angle

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.

Classify EHG, EFH, FHG by its angle measure

Triangle EHG is right

Triangle EFH is obtuse

Triangle FHG is equiangular

Equilateral Triangle

Three congruent sides

Isosceles Triangle

At least two congruent sides

Scalene Triangle

No congruent sides

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.

Classify ABC, ABD and ACD by its side lengths.

ABC = equilateral Triangle ABD = Scalene

Triangle ACD = scalene

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

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

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:

Page 219: # 1-19

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

Classify each triangle by its angles and sides.

1. MNQ

2.NQP

3. MNP

4. Find the side lengths of the triangle.

Classify each triangle by its angles and sides.

1. MNQ

2.NQP

3. MNP

4. Find the side lengths of the triangle.