Geometry Fall emester Review (13-14) EEER REVIEW 1: hapters 1 and 2 1. What is Geometry? 2. What are the three undefined terms of geometry? 3. Find the definition of each of the following. a. Postulate b. heorem 4. Given points and. What symbol is used to describe the following? a. the segment b. the ray from point passing through c. the line passing through points and d. the distance of the segment 8. Refer to the points on a number line. V -12-6 0 4 10 a. Find each of the following. Use formula: a b V =, =, + V = b. Point is between and some point. is twice as long as, what is the coordinate of? 9. Given: coordinates of N are (-5, -1) and N(3, 5). a. Graph segment N. 5. olve for area,, or perimeter, P. a. Rectangle given: L = 9.1 cm and P = 29cm. Find the width and the area. b. riangle given: height is cm, base is 7 cm, and area is 30 cm 2. he triangle is a right triangle. b. What are the coordinates of the midpoint of N? Hint: use the midpoint formula. 6. Use the egment ddition Postulate: is between and. If = 3 5, = + 7, and = 26, find the each of the following. c. What is the length of N? Hint: use the distance formula. a. the value of b. = 7. Use the idpoint heorem: is between and. If = 5 3, = + 13, find the each of the following. 10. Point D is the midpoint of E. he coordinates of point is (-2, 3) and point D is (5, -1) Find the coordinates of the other endpoint E. a. the value of b. =
11. Refer to the figure. E D a. Write each angle described: acute, obtuse, right b. Name a pair of each described angle: a pair of vertical angles a linear pair / supplementary a pair of complementary angles O 15. Refer to an If-hen statement: If P, then Q. Write each of the following. a. the hypothesis b. the conclusion c. the converse d. the inverse e. the contrapositive 16. Refer to an If-hen statement: If it is hristmas, then I ll receive presents. 12. omplete the following proof: Given: R = 5, R = 5, R Prove: R tatements Reasons R Write each of the following. a. the hypothesis b. the conclusion c. the converse d. the inverse 13. Given: OQ bisects POR, m POQ = 5 9, and m QOR = + 23. a. find the value of, e. the contrapositive b. m POQ c. m POR. 17. he measure of an angle is 40 less than its supplement. Find the measure of the angles. 14. Name the Property of Equality using the segments:, D, EF, and GH. a. 18. he measure of an angle is 9 more than twice its complement. Find the measure of the angles. b. If = D, then D = c. If = D and D = EF, then = EF d. If + EF = F and EF = 8, then + 8 = F e. If + 15 = D, then + 22 = D + 7 19. Given: O and O are supplementary angles. If m O is 30 less than twice m O, find measures of angles O and O. f. If EF 4 = GH, 5(EF 4) = 5GH
Geometry Fall emester Review (12-13) EEER REVIEW 2: hapters 3 and 4 1. In the figure, assume all angles are 90. Find the each of the following. Q R P N O L Write if the statement is true. Write F otherwise. a) P / / QR b) OP ON c) PQ intersect plane RN at. d) L and N are skew segments. 2. Refer to lines L1 and L2 and transversals 1 and 2. Name each of the angle pair as: corresponding angles, alternate interior angles, alternate eterior angles, consecutive interior angles, or vertical angles. 5 6 8 7 1 4 2 3 9 10 12 11 15 16 14 13 a. 2 and 6 b. 9 and 16 4. Determine if lines L1 and L2 are parallel, perpendicular, or neither. Verify by comparing the slopes. Write the slope formula and show your work. Line L1 has points (5, 3) and (0, 13). Line L2 has points (2, -3) and D(10, 1). L1: m =, L2: m = re they parallel or perpendicular? 5. Write the equation of the line in slope-intercept form, y = m + b, given the following information. 3 a line that has a slope and y-intercept 8 4 Equation: 6. Write the equation describing a line that passes through (1, 4) and is parallel to the line represented by the equation 2 y = 4. Equation: 7. Write the equation describing a line that passes through (6, 3) and is perpendicular to the line represented by the equation 2 3y = 9. c. 4 and 8 d. 5 and 7 e. 11 and 13 3. Given: p // q. Find the measure of each angle. Equation: 8. Graph the lines y = 2 3 2 and y = 3 + 2 2 p 6 2 5 4 q t1 118 1 3 144 t2 a. m 1 = b. m 2 = c. m 3 = d. m 4 = e. m 5 = f. m 6 = re the lines parallel or perpendicular?
9. atch the triangle.... D. E. F. 16. Decide whether the triangles are congruent. Justify by,,,, or HL Postulate. Write NP if not congruent. a. scalene/obtuse c. isosceles/acute e. scalene/acute b. isosceles/right d. equilateral f. scalene/right a. b. 10. In, m = 9, m = 5 5, and m = 2 + 25. c. d. a. Find the value of. b. lassify. 11. Refer to the figures. Find the value of. e. f. a. b. 25 22 35 3 (5 + 15) 17. What is the rate of change of the function? = 4 12. Given: LN PQR, L = 5 3, QR = 3, PR = + 6, and PQ = 2 + 9. a. Find the value of, b. Find the perimeter of LN. 18. omplete the following proof: Given: PQ bisects <P, P P P Prove: 13. Given: D. Fill in the blanks. a.. b. D. c. D. d. D. e. D. D tatements Q Reasons 14. R is an isosceles triangle. Its perimeter is 33 cm, R = 2 1, R = + 10, and = 3 6. a. Find the value of. b. How much longer is the base to its leg? 15. Find the values of and y. a. = 38 y = y
Geometry Fall emester Review (12-13) EEER REVIEW 3: hapters 5 and 6 1. he special segments in are shown with dashed line. = and m O = m O. Identify the following. a. the median b. the altitude L c. the angle bisector d. the perpendicular bisector e. Which special segments do not always contain a verte? N O 5. Determine if the lengths could be the sides of a triangle? Write yes or no. a. 17, 30, 13 b. 58, 22, 40 c. 1.4, 5.2, 3.6 6. Find the possible length of the third sides of the triangle given the length of the two sides a. 12 and 23 b. 8 and 34 2. is the altitude, the median, and the angle bisector in Z. a. If m = 65, find m Z. b. If = 7, find Z. c. Find m Z. d. Prove that is a perpendicular bisector in Z. Z 7. Refer to the figure. rrange the angles of the triangle from least to greatest measure. J 34 28 L 22 K ngles:,, 8. Refer to the figure. rrange the sides of the triangle from shortest to longest. H 3. Refer to the diagram. Points, N, and P are the midpoints of,, and in. ides:,, I 64 57 G N P a. If = 24, then N =. b. If NP = 14, then =. c. If P = 10 and = 2 8, then. d. If P = 10, NP = 14, and N = 12, find the perimeter of. 4. is the centroid of. 9. Given: R is the median in U. a. Find the value of. b. Find R. c. Find U. d. Find. 5 2 + 5 U R + 13 a. If = 24, then =. b. If = 20, then =. c. If Z = 7, then =. Z 10. Refer to the figure. omplete the statement with >, <, or =. G H 59 GH JI. 62 J I
11. he perimeter of a rectangle is 36 inches. he ratio of its length and width is 4 : 5. Find the length and the width, and the area of this rectangle. a. length = b. width = c. rea = 14. lyssa wants to measure the height of the flagpole school. he places a mirror on the ground 54 feet from the flagpole, then walks backward until she is able to see the top of the flagpole in the mirror. Her eyes are 5.9 feet above the ground, and she is 14 feet from the mirror. What is the height of the flagpole to the nearest tenth of a foot? 12. Refer to the similar triangles. 10 7 Given: Z. y 18 14 Z 15. egments a, b, and c are parallel. Find the value of. a 27 a. Write all pairs of congruent angles. b c 20 23 b. Write the ratios of proportional sides. = = c. What is the scale factor of to Z?. F. = Image Original = d. Write a proportion to solve for the values of and y. hen, find and y. y = 16. Given: DE (not drawn to scale). = 8, and E = 12. D 8 12 E If the perimeter of triangle = 20, what is the perimeter of triangle DE answer 13. Given: R RUV. R 18 6 U Write a proportion to solve for the values of and y. hen, find and y. 12 21 y V 17. Given: ED (not drawn to scale). = 1.5, = 2, and DE = 4.5. E 4.5 1.5 2 D a. What is the perimeter of triangle DE? answer y =
Geometry Fall emester Review (12-13) EEER REVIEW Etra: ransformations 1. he vertices of Δ are (2, 3), (1, 0), and (-2, 4). Graph the image of Δ after the translation (, y) ( + 3, y 2). 2. Graph the reflection of the polygon in the given line. a. = 4 b. -ais ( = 0) 5. Using the oordinate Rules for Rotations about the origin where would the following points end up? () For a rotation of 90, (5, 2) (, ) () For a rotation of 180, (6, -3) (, ) () For a rotation of 270, (8, 9) (, )