# Geometry Semester 1 REVIEW Must show all work on the Review and Final Exam for full credit.

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1 Geometry Semester 1 REVIEW Must show all work on the Review and Final Exam for full credit. NAME UNIT 1: 1.6 Midpoint and Distance in the Coordinate Plane 1. What are the coordinates of the midpoint of GH with endpoints G( 2, 5) and H(4, 1)? 2. Use the Distance Formula to find VW. 3. Use the Pythagorean Theorem the find the exact simplified length of the hypotenuse. 10 cm 3.5/3.6 Slopes of Lines/Lines in the Coordinate Plane 4. Find the slope of the line that passes through the points (-2,4) and (6,8). 4. m= 5. Write the equation of the line through (-6,-2) and (3,4) in point-slope form and slope-intercept form. m = Point-slope form Slope-int. form

2 6. Use the slopes to determine if AB and CD are parallel, intersecting, or perpendicular. A(4,-1); B(1,-1); C(5,1); D(5,-2). AB : m = CD : m = 7. Determine whether 6x + y = 3 and 12x + 2y = 6 are parallel, intersecting, perpendicular, or coinciding /10.2 Area and Perimeter Formulas: Triangles, Quadrilaterals, Circles, and Regular Polygons 8. Find the area of the following rhombus. Round to the nearest hundredth. 6 m 20 m 6 m 9. Find the height of the isosceles trapezoid if the area is 96 ft 2 10 ft 22 ft 10. Find the area and of kite EFGH. Round to the nearest hundredth What is the area of a triangle with a height of 3 inches and a base of 5.5 inches? 12. A circle has a diameter of 10 feet. What is its approximate area?

3 13. Find the missing values below. Write the answer in terms of. 7 in Area 16 miles Area = Circumference = radius = Circumference = 14. Find the area of the regular pentagon. 10 in 8 in Find the area of the regular hexagon. Round to the nearest tenth Perimeter and Area in the Coordinate Plane 16. Find the perimeter of the polygon with vertices A(-4, 1), B(2, 4), C(0, 4), and D(-2, -3). y Round your answers to the nearest tenth. x

4 UNIT 2: 9.1/9.2/9.3/9.4/9.5/9.7 Transformations and Compositions of Transformations Identify the type of transformation Draw the reflection of the figure across the line. A 20. B D g C 21. Given points P(-2, -1) and Q(-1, 3), graph the primage and image after reflection across the y-axis. (x, y) ( ) P(-2, -1) P ( ) Q(-1, 3) Q ( ) 22. A figure has vertices at E(2, 0), F(2, -1), G(5, -1), and H(5, 0). After a transformation, the image of the figure has vertices at E (0, 2), F (1, 2), G (1, 5), and H (0, 5). Draw the preimage and image. Then identify the transformation.

5 23. A figure has vertices at G(0, 0), H(-1, -2), I(2, 0), and J(3,- 2). Graph the preimage and image after a translation left 2 units and up 4 units. (x, y) ( ) G(0, 0) ( ) G ( ) H(-1, -2) ( ) H ( ) I(2, 0) ( ) I ( ) J(3,- 2) ( ) J ( ) 24. A figure has vertices at X(-1,-2), Y(2, 0), and Z(3, -2). Draw the image of XYZ after the translation (x, y) (x +2, y) and then a 180 rotation around the origin. (x, y) ( ) ( ) X(-1, -2) ( ) X ( ) X ( ) Y(2, 0) ( ) Y ( ) Y ( ) Z(3,- 2) ( ) Z ( ) Z ( ) Write the translation rule. 25. Every point moves right 3 units and down 4 units. (x, y) ( ) 26. Every point moves left 8 units. (x, y) ( ) 27. Figure WXYZ is rotated 90 counterclockwise. List the new points and graph the preimage and image. (x, y) ( ) W(2, 2) W ( ) X(0, 4) X ( ) Y( 1, 3) Y ( ) Z(1, 1) Z ( )

6 28. Graph the image of ABC after the given glide reflection: Translation: (a, b) (a 2, b + 3) Reflection: over the x-axis. y (x, y) ( ) ( ) A A( ) ( ) A ( ) A ( ) B( ) ( ) B ( ) B ( ) C B x C( ) ( ) C ( ) C ( ) 29. Graph MN with M (1, 2) and N (2, 3). Then graph its dilation with a scale factor of 1.5 centered at (0,0). Give the new coordinates: (x, y) ( ) y M(1, 2) ( ) N(2, 3) ( ) x 30. Draw the image of the given figure after a dilation of with scale factor -2 and centered at O. (x, y) ( ) y A( 3, 2) A'( ) B( 3, 3) B'( ) C(1, 2) C'( ) D(1, 4) D'( ) x UNIT 3: 1.2/1.3/1.4 Measuring Segments and Angles, Pairs of Angles 31. What is the measure of RT?

7 32. Which term describes PMQ? 33. What is m PMN? 34. Identify each angle pair as adjacent, linear pair, vertical angles or none. a) 1 and 2 b) 1 and 5 c) 3 and 4 d) 1 and 4 e) 1 and What is m WXY? 36. If m A 47, what is the measure of a complement of A? 3.1 Lines and Angles 3.2 Angles Formed by Parallel Lines and Transversals For numbers 37-39, use the figure to identify each of the following. C B D A 37. a pair of parallel segments: 38. a pair of skew segments: E 39. a pair of perpendicular segments: G F

8 For numbers 40-44, classify each angle pair as corresponding angles, alternate interior angles, alternate exterior angles, same side interior angles or none. t and 10: and 4: p and 11: and 12: Solve for x and find each angle measure. m and 1: a. x = (2x+20) A (4x-80) C b. m ABH c. m CDF = = H B D F E S 46. Solve for x and find each angle measure. S K 12x A (3x-40) 46 a. x = b. m STA = c. m KAT = T (2x +20) E D 4.2/4.3 Classifying Triangles For numbers 47-50, classify the triangle by its sides and angles

9 For numbers 51-54, find the measure of each angle indicated m B= 52. m F 53. m L 54. m VWY For numbers 55 and 56 solve for x. 55. x = 56. x = The measure of one of the acute angles in a right triangle is given. Find the measure of the other acute angle (x + 3)

10 2.5 Algebraic Proofs For numbers 60-62, use a two-column chart to solve. 60. GIVEN: HI + IJ = HJ PROVE: x = GIVEN: ( 10) 3 5 a PROVE: a = GIVEN: t 6.5 3t 1.3 PROVE: t = 3.9

11 For numbers 63-66, identify the property that justifies each statement. 63. m n, so n m. 64. m ABC m ABC 65. KL LK 66. p = q and q = -1, so p = Geometric Proofs For numbers 67-71, complete each two-column proof. 67. Given: AB = EF, B is the midpoint of AC, and E is the midpoint of DF. Prove: DE BC 68. Given: 1 is complementary to 2 3 is complementary to 2 Prove:

12 69. Given: A triangle with interior angles 1, 2 and 3. 4 is exterior to 3. (You can t use Exterior Angle Theorem) Prove: m 4 = m 1 + m A 70. Given: MAD BAC Prove: 1 3 M B D C

13 71. Given: 1 4 Prove: 2 3 (NOTE: You may not use the Vertical Angles Thereom) UNIT 4-4.5/4.6/4.7 Triangle Congruency 72. List the 5 methods (theorems/postulates) you know to prove two triangles are congruent. For numbers 73-78, state if the two triangles are congruent. If they are, state how you know. If not, say not congruent

14 79. CPCTC is an abbreviation of the phrase Corresponding of Congruent are Congruent. For numbers 80-82, complete the two-column proofs. 80. Given: JL bisects KLM; K M Prove: JKL JML 81. Given: GJ bisects FGH, FG HG Prove: FJ HJ

15 82. Given: J L Prove: LK JM

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