Geometry Regents Review # 3

Transcription

1 Geometry Regents Review # 3 Name: ate: 1. If the angles of a triangle are represented by x, 3x + 20, and 6x, the triangle must be 3. In an isosceles triangle, the ratio of the measure of the vertex to the measure of a base angle is 1 : 4. Find the measure of the vertex angle.. obtuse B. right. acute. isosceles 2. If the midpoints of two consecutive sides of a rhombus are joined, the triangle formed must be 4. right triangle contains a 38 angle whose adjacent side measures 10 centimeters. What is the length of the hypotenuse, to the nearest hundredth of a centimeter?. isosceles B. acute B equilateral. right page 1

2 . In the diagram below, LMO is isosceles with LO = MO. 7. Tina wants to sew a piece of fabric into a scarf in the shape of an isosceles triangle, as shown in the accompanying diagram. What are the values of x and y? If m L = and m NOM = 28, what is m N?. 27 B x = 42 and y = 96 B. x = 69 and y = 69. x = 90 and y = 48. x = 96 and y = In the accompanying diagram of B, is extended to, EF, BE, FB, m B = 0, m BEF = 2, and m B = 6. What is m?. 40 B billboard on level ground is supported by a brace, as shown in the accompanying diagram. The measure of angle is 1 greater than twice the measure of angle B. etermine the measure of angle and the measure of angle B.. 0. page 2 Geometry Regents Review # 3

3 9. Side PQ of PQR is extended through Q to point T. Which statement is not always true? 11. B is similar to EF. The ratio of the length of B to the length of E is 3 : 1. Which ratio is also equal to 3 : 1?. m RQT > m R B. m RQT > m P. m RQT = m P + m R. m RQT > m PQR. B... m m m B m F area of B area of EF perimeter of B perimeter of EF 10. In the diagram below of B, is the bisector of B, E is the bisector of B, and BG is drawn. 12. In the diagram below of B, is the midpoint of B, and E is the midpoint of B. Which statement must be true?. G = EG B. G = BG. EB = E. BG = EBG If = 4x + 10, which expression represents E?. x + 2. B. 2x +. 2x x + 20 page 3 Geometry Regents Review # 3

4 13. In the diagram below of right triangle B, is the altitude to hypotenuse B, B = 6, and =. 1. In the diagram below of, B is a point on such that B is an equilateral triangle, and B is an isosceles triangle with B = B. Find m. What is the length of B?. B In the diagram below of B, side B is extended to point, m = x, m B = 2x + 1, and m = x The sum of the interior angles of a polygon of n sides is. 360 B.. (n 2) n (n 2) 180 n What is m B?. B page 4 Geometry Regents Review # 3

5 17. In the diagram below of B, B is extended to. 19. On the set of axes below, the vertices of PQR have coordinates P( 6, 7), Q(2, 1), and R( 1, 3). If m = x 2 6x, m B = 2x 3, and m = 9x + 27, what is the value of x?. 10 B What is the area of PQR?. 10 B In B shown below with, EB, FE, and BF, E = B. 20. In the diagram below, right triangle B has legs whose lengths are 4 and 6. Which statement must be true?. F = BF B. E = FE. B = B. EF = F What is the volume of the three-dimensional object formed by continuously rotating the right triangle around B?. 32π B. 48π. 96π. 144π page Geometry Regents Review # 3

6 21. To build a handicapped-access ramp, the building code states that for every 1 inch of vertical rise in height, the ramp must extend out 12 inches horizontally, as shown in the diagram below. 24. s modeled below, a movie is projected onto a large outdoor screen. The bottom of the 60-foot-tall screen is 12 feet off the ground. The projector sits on the ground at a horizontal distance of 7 feet from the screen. What is the angle of inclination, x, of this ramp, to the nearest hundredth of a degree? B etermine and state, to the nearest tenth of a degree, the measure of θ, the projection angle. 22. In B, where is a right angle, 21 cos =. What is sin B?. 21 B n equilateral triangle has sides of length 20. To the nearest tenth, what is the height of the equilateral triangle? B page 6 Geometry Regents Review # 3

7 Problem-ttic format version c Educide Software Licensed for use by Jen alderon Terms of Use at Geometry Regents Review # 3 /18/ B 8. m = 6 and m B = B