1.
\(\)DFG\(\) is a straight line. What is the value of \(\)x\(\)?
A. 12
B. 14
C. 16
D. 18
E. 20
2. If the hypotenuse of an isosceles right triangle is \(\)7\sqrt { 2 }\(\) , what is the area of the triangle?
(A) \(\)14\(\)
(B) \(\)18\(\)
(C) \(\)24.5\(\)
(D) \(\)28\(\)
(E) \(\)49\(\)
3. If \(\)p\(\) is the perimeter of a triangle with one side of \(\)6\(\) and another side of \(\)9\(\), what is the range of possible values for \(\)p\(\)?
(A) \(\)3 < p < 15\(\)
(B) \(\)15 < p < 24\(\)
(C) \(\)18 < p < 30\(\)
(D) \(\)18 < p < 42\(\)
(E) \(\)21 < p < 42\(\)
4. A triangle has sides of \(\)8, m\(\), and \(\)n\(\).
| Quantity A | Quantity B |
| |\(\)m-n\(\)| | \(\)8\(\) |
5.
| Quantity A | Quantity B |
| The clockwise angle made by the hour hand and the minute hand at \(\)12:15\(\)pm | The counterclockwise angle made by the hour hand and the minute hand at \(\)12:45\(\)pm |
6. A \(\)10\(\) foot ladder leans against a vertical wall and forms a \(\)60\(\) degree angle with the floor. Assuming the ground below the ladder is perfectly horizontal, how far above the ground is the top of the ladder?
(A) \(\)5\(\) feet
(B) \(\)5\sqrt { 3 }\(\) feet
(C) \(\)7.5\(\) feet
(D) \(\)10\(\) feet
(E) \(\)10\sqrt { 3 }\(\) feet
7. In the figure, if line \(\)CE\(\) bisects ∠\(\)ACB\(\), then \(\)x\(\) =
(A) \(\)45\(\)
(B) \(\)50\(\)
(C) \(\)55\(\)
(D) \(\)65\(\)
(E) \(\)70\(\)
8. In the triangle, what is the value of \(\)x\(\) ?
(A) \(\)25\(\)
(B) \(\)55\(\)
(C) \(\)60\(\)
(D) \(\)77\(\)
(E) \(\)85\(\)
9. The following are the measures of the sides of five different triangles. Which one of them represents a right triangle?
(A) \(\)\sqrt { 3 },\sqrt { 4 },\sqrt { 5 }\(\)
(B) \(\)1, 5, 4\(\)
(C) \(\)7, 3, 4\(\)
(D) \(\)\sqrt { 3 },\sqrt { 7 },\sqrt { 4 }\(\)
(E) \(\)4, 8, 10\(\)
10. In the figure, \(\)ABC\(\) and \(\)ADC\(\) are right triangles. Which of the following could be the lengths of \(\)AD\(\) and \(\)DC\(\), respectively?
(I) \(\)3\(\) and \(\)4\(\)
(II) \(\)4\(\) and \(\)6\(\)
(III) \(\)1\(\) and \(\)24\(\)
(IV) \(\)1\(\) and \(\)26\(\)
(A) I and II only
(B) II and III only
(C) III and IV only
(D) IV and I only
(E) I, II and III only
11.
| Quantity A | Quantity B |
| \(\)X\(\) | \(\)Y\(\) |
12.
| Quantity A | Quantity B |
| \(\)\frac { x }{ y }\(\) | \(\)1\(\) |
13.
Which of the following statements individually provide(s) sufficient additional information to determine the area of triangle \(\)ABC\(\) above?
Indicate all such statements.
(A) \(\)DBC\(\) is an equilateral triangle.
(B) \(\)ABD\(\) is an isosceles triangle.
(C) The length of \(\)BC\(\) is equal to the length of \(\)AD\(\).
(D) The length of \(\)BC\(\) is \(\)10\(\).
(E) The length of \(\)AD\(\) is \(\)10\(\).
14. In the figure below, \(\)AB=BC=CD\(\). If the area of triangle \(\)CDE\(\) is \(\)42\(\), what is the area of triangle \(\)ADG\(\)?
15. What are the lengths of sides \(\)NO\(\) and \(\)OP\(\) in triangle \(\)NOP\(\) below?
Answers:
1 \(\)20\(\)
2 C
3 C
4 |\(\)m-n\(\)|<\(\)8\(\)
5 B
6 B
7 D
8 A
9 D
10 C
11 D
12 A
13 A and D
14 \(\)378\(\)
15 \(\)NO=30\(\) and \(\)OP=10\sqrt { 34 }\(\)
