Math 8

Mr. Dixon

Warm UpSolve each equation.

1. 62 + x + 37 = 180

2. x + 90 + 11 = 180

3. 2x + 18 = 180

4. 180 = 2x + 72 + x

x = 81

x = 79

x = 81

x = 36

An acute triangle has 3 acute angles. A right triangle has 1 right angle. An obtuse triangle has 1 obtuse angle.

Example 1: Finding Angles in Acute, Right, and

Obtuse Triangles

Find c° in the right triangle.

42° + 90° + c° = 180°

132° + c° = 180°

c° = 48°

–132° –132°

Example 2: Finding Angles in Acute, Right, and

Obtuse Triangles

Find m° in the obtuse triangle.

23° + 62° + m° = 180°

85° + m° = 180°

m° = 95°

–85° –85°

Additional Example 3: Finding Angles in Acute, Right

and Obtuse Triangles

Find p° in the acute triangle.

73° + 44° + p° = 180°

117° + p° = 180°

p° = 63°

–117° –117°

Equilateral triangle has 3 congruent sides and 3 congruent angles.

Isosceles triangle has at least 2 congruent sides and 2 congruent angles.

Scalene triangle has no congruent sides and no congruent angles.

Additional Example 4: Finding Angles in Equilateral,

Isosceles, and Scalene Triangles

62° + t° + t° = 180°

62° + 2t° = 180°

2t° = 118°

–62° –62°

Find the angle measures in the isosceles triangle.

2t° = 118°2 2

t° = 59°

Triangle Sum Theorem

Combine like terms.

Subtract 62° from both sides.

Divide both sides by 2.

The angles labeled t° measure 59°.

Additional Example 5: Finding Angles in Equilateral,

Isosceles, and Scalene Triangles

2x° + 3x° + 5x° = 180°

10x° = 180°

x = 18°

10 10

Find the angle measures in the scalene triangle.

Triangle Sum Theorem

Combine like terms.

Divide both sides by 10.

The angle labeled 2x° measures 2(18°) = 36°, the angle labeled 3x°measures 3(18°) = 54°, and the angle labeled 5x° measures 5(18°) = 90°.

Additional Example 6: Finding Angles in Equilateral,

Isosceles, and Scalene Triangles

Find the angle measures in the equilateral triangle.

3b° = 180°

b° = 60°

3b° 180°

3 3=

Triangle Sum Theorem

All three angles measure 60°.

Divide both sides by 3.

Tell whether a triangle can have sides with the given lengths. Explain.

Find the sum of the lengths of each pair of sides and compare it to the third side.

Example 7: Using the Triangle Inequality Theorem

8 ft, 10 ft, 13 ft

8 + 10 > 13?

18 > 13

10 + 13 > 8?

23 > 8

8 + 13 > 10?

21 > 10

A triangle can have these side lengths. The sum of the lengths of any two sides is greater than the length of the third side.

Pg. 345 (1 – 21) All; (36 – 45) All

Calculators may be used.

All work must be shown.