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 90 o 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 EQUIANGULAR ACUTE 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

1-1A

1-3A Slide 3 of 3

1-3B Slide 3 of 3

1-3C Slide 3 of 3

1-3D Slide 3 of 3

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

5-2 ANGLES OF A TRIANGLE

1-1A Slide 1 of 2

1-2A Slide 2 of 2

1-2B Slide 2 of 2

1-2C Slide 2 of 2

1-2D Slide 2 of 2

1-2D Slide 2 of 2

1-2E Slide 2 of 2

1-2E Slide 2 of 2

1-2F Slide 2 of 2

1-2G Slide 2 of 2

1-2H Slide 2 of 2

1-2I Slide 2 of 2

1-2J Slide 2 of 2

1-2J Slide 2 of 2

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 2 Substitute 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 2x2x 3x3x 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