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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
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Find mDBC
200
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Find mCAD & mACB
900mCAD = _______ mACB = ______1350
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Find the value of x and y.
x = ____ y = ____ 650 500
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Find m and n.
m = ____ n = ____ 440 680
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Solve for x, each side, classify.
mACB = ____ mBAC = ____650 500
A
BC 650
Classify by sides: _______ Classify by angles: ______Isosceles Acute
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Find the value of x and y.
x = ____ y = ____ 30 20
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Solve for x and each side.
x = ____ AB = ____ BC = ____ AC = ____4 12
4x + 8 3x + 12
6x
12 12
A
BC
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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
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Solve for x and each angle.
x = ___ BAC = ___ ABC = ___ ACB = ___17 450 450
A
BC
(3x – 6)0
900
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Solve for x and each side.
x = ____ AC = ____ BC = ____ AB = ____-5 30 30
A
BC
-5x + 5
42.4
-2x + 20
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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
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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.
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x + 7 = 55
x = 48
55 + (48 + 7) + y = 180
110 + y = 180
y = 170
Find the value of x and y.
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x = 45
9y = 45
y = 5
Find the value of x and y.
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Find the value of x.This is an isosceles triangle, so the 2 sides are congruent…
5x + 5 = 35
5x = 30
x = 6
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This is an isosceles triangle, so the 2 angles are congruent…
9x = 72
x = 8
Find the value of x.
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x + x + 102 = 180
2x + 102 = 180
2x = 78
x = 39
Find the value of x.
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Find the value of x and y.
3x – 11 = 2x + 11
x = 22
2y = 70y = 35
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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