the wall at the front entrance to the rock and roll hall of fame and museum in cleveland, ohio, is...

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. 102 0 39 0 39 0

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Page 1: 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

Draw a labeled picture. 1020

390 390

Page 2: 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

Find mDBC

200

Page 3: 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

Find mCAD & mACB

900mCAD = _______ mACB = ______1350

Page 4: 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

Find the value of x and y.

x = ____ y = ____ 650 500

Page 5: 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

Find m and n.

m = ____ n = ____ 440 680

Page 6: 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

Solve for x, each side, classify.

mACB = ____ mBAC = ____650 500

BC 650

Classify by sides: _______ Classify by angles: ______Isosceles Acute

Page 7: 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

Find the value of x and y.

x = ____ y = ____ 30 20

Page 8: 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

Solve for x and each side.

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

4x + 8 3x + 12

12 12

Page 9: 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

Solve for x, each side, classify.

x = ____ AB = ____ AC = ____12 66

3(2x – 2) 5x + 6

390

BC 390

Classify by sides: _______ Classify by angles: _______Isosceles Obtuse

Page 10: 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

Solve for x and each angle.

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

(3x – 6)0

900

Page 11: 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

Solve for x and each side.

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

-5x + 5

42.4

-2x + 20

Page 12: 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

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

x = 33.9

Page 13: 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

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.

Page 14: 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

x + 7 = 55

x = 48

55 + (48 + 7) + y = 180

110 + y = 180

y = 170

Find the value of x and y.

Page 15: 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

x = 45

9y = 45

y = 5

Find the value of x and y.

Page 16: 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

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

5x + 5 = 35

5x = 30

x = 6

Page 17: 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

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

9x = 72

x = 8

Find the value of x.

Page 18: 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

x + x + 102 = 180

2x + 102 = 180

2x = 78

x = 39

Find the value of x.

Page 19: 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

Find the value of x and y.

3x – 11 = 2x + 11

x = 22

2y = 70y = 35

Page 20: 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

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

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