Lesson 4-1

Classifying Triangles

5-Minute Check on Chapter 35-Minute Check on Chapter 35-Minute Check on Chapter 35-Minute Check on Chapter 3 Transparency 4-1

Refer to the figure.1. What is the special name given to the pair of angles

shown by 2 and 6?

2. Find m3.

3. Find m4.

4. Find the slope of the line that contains the points at (4, 4) and(2, –5).

5. Write the equation of a line in slope-intercept form that has a slope of¾ and contains the point at (0, 5).

6. What is the slope of a line that is perpendicular to the line y = 2/3x – 5?Standardized Test Practice:

A CB D–3/2 –2/3 2/3 3/2

5-Minute Check on Chapter 35-Minute Check on Chapter 35-Minute Check on Chapter 35-Minute Check on Chapter 3 Transparency 4-1

Refer to the figure.1. What is the special name given to the pair of angles

shown by 2 and 6? corresponding angles

2. Find m3. 62

3. Find m4. 118

4. Find the slope of the line that contains the points at (4, 4) and(2, –5). 9/2

5. Write the equation of a line in slope-intercept form that has a slope of¾ and contains the point at (0, 5). y = 3/4x + 5

6. What is the slope of a line that is perpendicular to the line y = 2/3x – 5?Standardized Test Practice:

A CB D–3/2 –2/3 2/3 3/2

Objectives

• Identify and classify triangles by angles

• Identify and classify triangles by sides

Vocabulary

• Scalene – no sides are congruent

• Isosceles – two sides are congruent

• Equilateral – all sides are congruent

• Equiangular – all angles are congruent

Classifying Triangles… By angles

… By sides

Acute triangle Obtuse triangle Right triangle

Scalene triangle Isosceles triangle Equilateral triangle

All angles < 90 One angle > 90 One angle = 90

No sides are Two sides are All sides are

Classifying TrianglesClassify by angle measure

Classify by number of congruent sides

Angles Sides

Measure of one angle

is 90°

Measure of all angles

< 90°

Measure of one angle

> 90°

No sidescongruent

2 sidescongruent

3 sidescongruent

Right

Obtuse

Acute

Scalene

Isosceles

EquilateralEquiangular3 congruent

angles

ARCHITECTURE The triangular truss below is modeled for steel construction. Classify JMN, JKO, and OLN as acute, equiangular, obtuse, or right.

Answer:JMN has one angle with measure greater than 90, so it is an obtuse triangle.

JKO has one angle with measure equal to 90, so it is a right triangle.

OLN is an acute triangle with all angles congruent, so it is an equiangular triangle.

ARCHITECTURE The frame of this window design is made up of many triangles. Classify ABC, ACD, and ADE as acute, equiangular, obtuse, or right.

Answer: ABC is acute. ACD is obtuse. ADE is right.

Answer: UTX and UVX are isosceles.

Identify the indicated triangles in the figure if

Isosceles triangles have at least two sides congruent.

Isosceles triangles

Scalene triangles

Answer: VYX, ZTX, VZU, YTU, VWX, ZUX, and YXU are scalene.

Scalene triangles have no congruent sides.

Identify the indicated triangles in the figure.

a. isosceles triangles

b. scalene triangles

Answer: ABC, EBC, DEB, DCE, ADC, ABD

Answer: ADE, ABE

ALGEBRA Find d and the measure of each side of equilateral triangle KLM if KL = d + 2, LM = 12 – d and KM = 4d – 13.

Since KLM is equilateral, each side has the same length. So KL = KM.

Substitution

Subtract d from each side.

Add 13 to each side.

Divide each side by 3.

Next, substitute to find the length of each side.

Answer: For KLM, and the measure of each side is 7.

Answer:

ALGEBRA Find d and the measure of each side of equilateral triangle if and

COORDINATE GEOMETRY Find the measures of the sides of RST. Classify the triangle by sides.

Answer: ; since all 3 sides have different lengths, RST is scalene.

Use the distance formula to find the lengths of each side.

Find the measures of the sides of ABC. Classify the triangle by sides.

Answer: ; since all 3 sides have different lengths, ABC is scalene.

Summary & Homework

• Summary:– Triangles can be classified by their angles as

acute, obtuse or right – Triangles can be classified by their sides as

scalene, isosceles or equilateral

• Homework: – pg 238-9: 4-6, 9-11, 15-20, 32-35