5-1 Classifying Triangles

Today we will be learning how to classify triangles according to length of sides and measurement of the angles.

First we will learn to classify by the

ANGLES

Right triangles have ONE right angle

Acute Triangles have three acute angles

Smaller than 90o

Smaller than 90o

Smaller than 90o

Acute Angle

Obtuse Triangles have ONE obtuse angle

Obtuse Angle

We will now learn to classify triangles by their sides.

If you collapsed all of the sides they would form a line.

Equilateral Triangles have 3 equal sides

Isosceles Triangles have 2 equal sides.

Scalene Triangles have NO equal sides.

Classifying Triangles by Their Sides EQUILATERAL – 3 congruent sides

ISOSCELES – at least two sides

congruent

SCALENE – no sides congruent

EQUILATERAL

ISOSCELES

SCALENE

Classifying Triangles by Their Angles EQUIANGULAR – all angles are congruent

ACUTE – all angles are acute

RIGHT – one right angle

OBTUSE – one obtuse angle

EQUIANGULARACUTE

RIGHT

OBTUSE

Can You Classify the Different Triangles in the Picture Below?

Classify the following triangles: AED, ABC, ACD, ACE

Triangle AED = Equilateral, Equiangular

Triangle ABC = Equilateral, Equiangular

Triangle ACD = Isosceles, Obtuse

Triangle ACE = Scalene, Right

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You have now learned that triangles can be classified by either their sides or their angles.

5-2 ANGLES OF A TRIANGLE

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EXAMPLE 3 Find an angle measure

SOLUTION

STEP 1 Write and solve an equation to find the value of x.

Apply the Exterior Angle Theorem.(2x – 5)° = 70° + x°

Solve for x.x = 75

STEP 2Substitute 75 for x in 2x – 5 to find m∠JKM.

2x – 5 = 2 75 – 5 = 145

Find m∠JKM.

The measure of ∠JKM is 145°.ANSWER

GUIDED PRACTICE for Examples 3 and 4

Find the measure of 1 in the diagram shown.3.

The measure of ∠1 in the diagram is 65°.ANSWER

GUIDED PRACTICE for Examples 3 and 4

SOLUTION

A + B + C = 180°

x + 2x + 3x = 180°

6x = 180°

x = 30°

B = 2x = 2(30) = 60°

C = 3x = 3(30) = 90°

x

2x 3x

4. Find the measure of each interior angle of ABC, where m A = x , m B = 2x° , and m C = 3x°.°

GUIDED PRACTICE for Examples 3 and 4

5. Find the measures of the acute angles of the right triangle in the diagram shown.

26° and 64°ANSWER