: Select the best answer from the choices provided. (Each question is worth one point) 1. By what corollary is this true: AD/AB=AB/AC Leg-Hypotenuse geometric mean corollary Altitude-hypotenuse geometric mean corollary neither 2. If DC=12 cm and AD=3 cm, then BD=___. 4 cm 15 cm 6 cm 3. AD/AB=AB/AC. If AD=9 cm and DC=4 cm, then AB= ___ and BC= ___. 3 cm and 3√13 cm 3√13 cm and 2√13 cm 5 cm and 13 cm 4. ΔABC is a right triangle and DB is the altitude to hypotenuse AC. If DB=10 cm and CD=20 cm, find AB. 50 cm 5√5 40 cm 5. If x is the geometric mean between q and r, solve x in terms of q and r. x=qr x=(qr)2 x=√(qr) 6. Consider the right triangle above. Side a has length √13 cm and side b has length 6 cm. Find the length of side c. √26 cm √19 cm 7 cm 7. Consider the following right triangle. Side a has length 5 cm and side c has length 2√10 cm. Find the length of side b. √50 cm √15 cm √65 cm 8. An isosceles triangle has a base of 8 m. The length of the altitude to the base is 3 m. Find the lengths of the congruent sides. 3 m 2√3 m 5 m 9. The length of one side of an equilateral triangle is 10 cm. Find the altitude of the triangle. 5 cm 5√5 cm 5√3 cm 10. Find the length of the altitude of an equilateral triangle if one side has a length of 6 cm. 3√5 cm 3√3 cm 6√2 cm 11. The hypotenuse of an isosceles right triangle is 8 inches. Find the length of the legs. 4√2 in 8 in 2√2 in 12. Find the altitude of an equilateral triangle if one of its sides measures 12 cm. 3√6 cm 6√3 cm 6√5 cm 13. The measurements of a rectangular box are: l=12 cm, w=4 cm, h=3 cm Find the length of the diagonal GC shown in the figure. 14 cm 15 cm 13 cm 14. Find the measure of the diagonal of one face of a cube whose side measures 12 cm. 12 cm 12√3 cm 12√2 cm 15. The roof of a schoolhouse is shaped like an isosceles triangle. The base of the triangle measures 8 meters and one side measures 5 meters. Find the altitude. 4 meters 3 meters 7 meters 16. A tent is pitched such that it creates an equilateral triangle. If each of the congruent sides measure 2 meters, what is the height of the tent? 2 m √2 m √3 m 17. An equilateral triangle has an altitude of 7 cm. Find the length of one side. 7√2 cm (14√3)/3 cm 7√3 cm 18. In an isosceles right triangle, one of the congruent sides has a measure 7 cm. Find the measure of the hypotenuse. 4√3 cm 7 7√2 cm 7√3 cm 4 19. The hypotenuse of an isosceles right triangle is 2 cm. Find the measure of one of its legs. √2 cm 2 cm √2/2 cm 20. If b=6√3 cm, then a=___ and c=___. 9 cm and 6√6 cm 9 cm and 12√3 cm 6 cm and 12 cm 21. If c=10 cm, then a=___ and b=___. 5√3 cm and 10√3 cm 5 cm and 5√3 cm 10√3 cm and 20 cm 22. If c=12√3 cm, then a=___ and b=___. 6√3 cm and 18 cm 6√3 cm and 24 cm 24 cm and 24√3 cm 23. A square h.

1. : Select the best answer from the choices provided. (Each
question is worth one point)
1.
By what corollary is this true: AD/AB=AB/AC
Leg-Hypotenuse geometric mean corollary
Altitude-hypotenuse geometric mean corollary
neither
2.
If DC=12 cm and AD=3 cm, then BD=___.
4 cm 15 cm
6 cm
3.
AD/AB=AB/AC. If AD=9 cm and DC=4 cm, then AB= ___ and
BC= ___.
3 cm and 3√13 cm 3√13 cm and 2√13 cm
5 cm and 13 cm

2. 4.
ΔABC is a right triangle and DB is the altitude to hypotenuse
AC. If DB=10 cm and CD=20 cm, find AB.
50 cm 5√5
40 cm
5. If x is the geometric mean between q and r, solve x in
terms of q and r.
x=qr x=(qr)2
x=√(qr)
6.
Consider the right triangle above. Side a has length √13 cm and
side b has length 6 cm. Find the length of side c.
√26 cm √19 cm
7 cm
7.
Consider the following right triangle. Side a has length 5 cm
and side c has length 2√10 cm. Find the length of side b.

3. √50 cm √15 cm
√65 cm
8.
An isosceles triangle has a base of 8 m. The length of the
altitude to the base is 3 m. Find the lengths of the congruent
sides.
3 m 2√3 m
5 m
9.
The length of one side of an equilateral triangle is 10 cm. Find
the altitude of the triangle.
5 cm 5√5 cm
5√3 cm
10. Find the length of the altitude of an equilateral triangle if
one side has a length of 6 cm.
3√5 cm 3√3 cm
6√2 cm
11. The hypotenuse of an isosceles right triangle is 8 inches.
Find the length of the legs.

4. 4√2 in 8 in
2√2 in
12. Find the altitude of an equilateral triangle if one of its
sides measures 12 cm.
3√6 cm 6√3 cm
6√5 cm
13.
The measurements of a rectangular box are:
l=12 cm, w=4 cm, h=3 cm
Find the length of the diagonal GC shown in the figure.
14 cm 15 cm
13 cm
14.
Find the measure of the diagonal of one face of a cube whose
side measures 12 cm.

5. 12 cm 12√3 cm
12√2 cm
15. The roof of a schoolhouse is shaped like an isosceles
triangle. The base of the triangle measures 8 meters and one
side measures 5 meters. Find the altitude.
4 meters 3 meters
7 meters
16. A tent is pitched such that it creates an equilateral triangle.
If each of the congruent sides measure 2 meters, what is the
height of the tent?
2 m √2 m
√3 m
17. An equilateral triangle has an altitude of 7 cm. Find the
length of one side.
7√2 cm (14√3)/3 cm
7√3 cm
18. In an isosceles right triangle, one of the congruent sides
has a measure 7 cm. Find the measure of the hypotenuse.
4√3 cm
7

6. 7√2 cm
7√3 cm
4
19. The hypotenuse of an isosceles right triangle is 2 cm. Find
the measure of one of its legs.
√2 cm 2 cm
√2/2 cm
20.
If b=6√3 cm, then a=___ and c=___.
9 cm and 6√6 cm 9 cm and 12√3 cm
6 cm and 12 cm
21.
If c=10 cm, then a=___ and b=___.
5√3 cm and 10√3 cm 5 cm and 5√3 cm
10√3 cm and 20 cm

7. 22.
If c=12√3 cm, then a=___ and b=___.
6√3 cm and 18 cm 6√3 cm and 24 cm
24 cm and 24√3 cm
23. A square has a diagonal of length 10 cm. What is the
perimeter of the square?
10√2 cm 20√2 cm
5√2 cm
24. What is the square of √10?
2√10 10
5
25. What is the square of 3√b?
3b 6b
9b
26. What is the perimeter of a square with a diagonal of 3√2?
3 12
18
27. What is the length of a diagonal of a square with a side of

8. length 8?
8 8√2
2
28. What is the length of the diagonal of a square with a 15-
decimeter side?
15√2 dm 15 dm
√2 dm
29. What is the length of one side of a square with a 16-
centimeter diagonal?
√12 cm 8√2 cm
√16 cm
30. The perimeter of a square is 48 m. What is the length of a
side and a diagonal?
10 m; 144 m 8 m; 12 m
12 m; 12√2 m
Part 2
Short Answer: Type your response in the text box below each
item. If necessary, spell out mathematical symbols. (Each
question is worth five points)
31.
In trapezoid NDKF, NL and DG are altitudes, m∠ F=45º,

9. m∠ K=30º, DG=8, and ND=10. Find DK, GK, FN, m∠ GDK,
m∠ FNL, and the perimeter.
32.
Given: ABCD is a trapezoid. ΔAYD is congruent to ΔBCY.
ABYD is a rhombus. AD=3 and AX=1. Find the length of all
sides and diagonals.