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The wall at the front entrance to the Rock and Roll Hall of Fame and Museum in Cleveland, Ohio, is an isosceles triangle. The triangle has a vertex angle of 102. What is the measure of the base angles?

Draw a labeled picture. 1020

390 390

Find mDBC

200

Find mCAD & mACB

900mCAD = _______ mACB = ______1350

Find the value of x and y.

x = ____ y = ____ 650 500

Find m and n.

m = ____ n = ____ 440 680

Solve for x, each side, classify.

mACB = ____ mBAC = ____650 500

A

BC 650

Classify by sides: _______ Classify by angles: ______Isosceles Acute


x = ____ y = ____ 30 20

Solve for x and each side.

x = ____ AB = ____ BC = ____ AC = ____4 12

4x + 8 3x + 12

6x

12 12

A

BC

Solve for x, each side, classify.

x = ____ AB = ____ AC = ____12 66

3(2x – 2) 5x + 6

390

66

A

BC 390

Classify by sides: _______ Classify by angles: _______Isosceles Obtuse

Solve for x and each angle.

x = ___ BAC = ___ ABC = ___ ACB = ___17 450 450

A

BC

(3x – 6)0

900

Solve for x and each side.

x = ____ AC = ____ BC = ____ AB = ____-5 30 30

A

BC

-5x + 5

42.4

-2x + 20

If the legs of a right, isosceles triangle each measure 24 inches, find the length of the hypotenuse. Round to the nearest tenth.

x 24

24

x = 33.9

Determine whether the given lengths are sides of a right triangle? Explain.

5.2, 6.5, 3.9

42.25 = 42.25

Yes, because a2 + b2 = c2.

x + 7 = 55

x = 48

55 + (48 + 7) + y = 180

110 + y = 180

y = 170


x = 45

9y = 45

y = 5


Find the value of x.This is an isosceles triangle, so the 2 sides are congruent…

5x + 5 = 35

5x = 30

x = 6

This is an isosceles triangle, so the 2 angles are congruent…

9x = 72

x = 8

Find the value of x.

x + x + 102 = 180

2x + 102 = 180

2x = 78

x = 39

Find the value of x.


3x – 11 = 2x + 11

x = 22

2y = 70y = 35

Check for right angles by checking the slopes. There is a right angle in the triangle if any of the slopes

are perpendicular.

The slope of OP is 2 – 0 – 2 – 0

= – 2.

The slope of OQ is 3 – 0 6 – 0

=21 .

PQO is a right triangle because the slopes of the legs have opposite signs and reciprocals which means they are perpendicular and form a right angle.

Using slopes, determine if PQO is a right triangle. Explain.

SOLUTION

Explanation