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 of 102. What is the measure of the base angles? Draw a labeled picture.
1020
390
390

2. Find mDBC
200

3. Find mCAD & mACB
900
1350
mCAD = _______ mACB = ______

4. Find the value of x and y.
650
500
x = ____ y = ____

5. Find m and n.
440
680
m = ____ n = ____

6. Solve for x, each side, classify.B
650
650
500
mACB = ____ mBAC = ____
Isosceles
Acute
Classify by sides: _______
Classify by angles: ______

7. Find the value of x and y. 30 20
x = ____ y = ____

8. Solve for x and each side.B 6x 12 12 12 4
x = ____ AB = ____ BC = ____ AC = ____

9. Solve for x, each side, classify.
390 B
390 66 12 66
x = ____ AB = ____ AC = ____
Isosceles
Obtuse
Classify by sides: _______
Classify by angles: _______

10. Solve for x and each angle.B C 17
450
450
900
x = ___ BAC = ___ ABC = ___ ACB = ___

11. Solve for x and each side.B C
-2x + 20 -5 30 30
42.4
x = ____ AC = ____ BC = ____ AB = ____

12. If the legs of a right, isosceles triangle each measure 24 inches, find the length of the hypotenuse. Round to the nearest tenth. x
x = 33.9 24 24

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

14. Find the value of x and y. x = 48 x + 7 = 55 55 + (48 + 7) + y = 180

15. Find the value of x and y.
x = 45
9y = 45
y = 5

16. Find the value of x.
This is an isosceles triangle, so the 2 sides are congruent…
5x + 5 = 35
5x = 30
x = 6

17. Find the value of x.
This is an isosceles triangle, so the 2 angles are congruent…
9x = 72
x = 8

18. Find the value of x.
x + x = 180
2x = 180
2x = 78
x = 39

19. Find the value of x and y.
3x – 11 = 2x + 11
x = 22
2y = 70
y = 35

20. Using slopes, determine if PQO is a right triangle. Explain.
SOLUTION
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 = 2 1 .
Explanation
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.