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Geometry Winter Review 2014-2015 Name: __________________________________________________ Date:_______________________ MAFS.912.G-CO.4.12 1. Below is a stage in the construction of a line segment congruent to AB with point C as one of the endpoints of the new line segment. A. B. C. D. Which of the following sentences describes the next step in the construction? Set the compass point on point B and adjust the compass width to point C. Mark a point on ̅̅̅̅ and adjust the compass width to point C from the point. ̅̅̅̅ and make two arcs on ̅̅̅̅ centered at the point. Mark a point on Set the compass point on point A and adjust the compass width to point B. A. B. C. D. MAFS.912.G-CO.1.2 2. Which of the following transformations does not preserve distance and angle measures? translation reflection rotation horizontal stretch MAFS.912.G-CO.2.6 3. Is triangle congruent to triangle ? A. Yes. Triangle STU was rotated clockwise 270° about point T, translated 7 units to the right, and translated 6 units down to create triangle WXY. B. Yes. Triangle STU was rotated clockwise 270° about point T, translated 4 units to the right, and translated 2 units down to create triangle WXY. C. No. Triangle STU is not congruent to triangle WXY. D. Yes. Triangle STU was rotated clockwise 90° about point T, translated 7 units to the right, and translated 6 units down to create triangle WXY. ANSWER KEY Geometry Winter Review 2014-2015 MAFS.912.G-CO.4.12 4. Amy made a mistake in creating a copy of ∠. What does she need to correct in the following construction for copying ∠ with point as the vertex of the new angle? A. B. C. D. The second arc should be centered at point J and pass through point A. The third arc should be centered at point K and pass through point E. The second arc should be centered at point H and pass through point A. The third arc should be centered at point K and intersect the second arc. MAFS.912.G-CO.1.3 5. If ∠ ≅ ∠, which of the following conditions must also be met to prove that ∆ ≅ ∆ by AngleAngle-Side rule? A. B. C. D. I only I or IV only II only III or IV only ANSWER KEY Geometry Winter Review MAFS.912.G-CO.1.3 6. Which transformation carries the regular hexagon EFGHIJ onto itself? A. B. C. D. a rotation of 60° about its center a rotation of 45° about its center a rotation of 90° about its center a rotation of 30° about its center MAFS.912.G-CO.3.10 7. Given: ∆ with exterior ∠4 Prove: ∠4 = ∠1 + ∠2 Proof: Which of the following reasons completes the proof? A. B. C. D. ∠4 + ∠3 = ∠1 + ∠2 + ∠4 ∠1 + ∠3 + ∠4 = 180° ∠1 + ∠2 + ∠4 = 180° ∠4 + ∠3 = ∠1 + ∠2 + ∠3 ANSWER KEY 2014-2015 Geometry Winter Review 2014-2015 MAFS.912.G-CO.2.7 8. Triangles ABC and DEF have two sets of sides of the same length and the included angles between those sides have the same measure as shown below. Which of the following point transformations is a result of a sequence of rigid motions that can be used to show that triangle ABC is congruent to triangle DEF by taking triangle ABC onto triangle DEF? A. B. C. D. (, ) (− + 7, −) (, ) (−, − + 7) (, ) (−, − + 7) (, ) (− + 7, −) MAFS.912.G-CO.4.12 9. What is the first step in the construction of an angle bisector using only a compass and straightedge? A. Mark a point in the angle's interior and draw an arc centered at the point, intersecting both the legs of the angle. B. Place the compass needle on one of the legs of the angle and draw an arc intersecting the other leg. C. Mark a point outside the angle and draw an arc centered at the point, intersecting the vertex of the angle. D. Place the compass needle on the vertex of the angle and draw an arc across both legs of the angle. MAFS.912.G-CO.2.7 10. A series of transformations were applied to triangle to create triangle . If triangle JKL and triangle XYZ are congruent, which of the following transformations could have been applied to triangle JKL? A. B. C. D. I and III only I, II, III, and IV I, II, and III only I and II only ANSWER KEY Geometry Winter Review MAFS.912.G-CO.3.9 11. Given: ∥ and u is a transversal of s and t. Prove: ∠1 ≅ ∠5, ∠2 ≅ ∠6, ∠3 ≅ ∠7, ∠4 ≅ ∠8 2014-2015 Proof: Which of the following reasons completes the proof? A. B. C. D. Two lines cut by a transversal which has a pair of congruent corresponding angles are parallel. Two lines cut by a transversal which has a pair of congruent exterior angles are parallel. Parallel angles postulate. Converse of the parallel angles postulate. MAFS.912.G-CO.1.2 12. Which of the following transformations will produce a similar, but not congruent figure? A. B. C. D. dilation reflection rotation translation ANSWER KEY Geometry Winter Review MAFS.912.G-CO.3.9 13. Given: ∠2 and ∠3 are a linear pair, ∠3 and ∠4 are a linear pair Prove: ∠2 ≅ ∠4 Proof: Which of the following reasons completes the proof? A. B. C. D. Transitive property Linear pair postulate Congruent complements theorem Right angle congruence theorem MAFS.912.G-CO.1.3 14. Which transformation carries the regular pentagon below onto itself? A. B. C. D. a rotation of 36° about the origin a rotation of 45° about the origin a rotation of 115° about the origin a rotation of 72° about the origin ANSWER KEY 2014-2015 Geometry Winter Review MAFS.912.G-CO.2.8 15. Triangle is rotated clockwise 90° to create triangle . 2014-2015 Is triangle MNO congruent to triangle UVW? A. B. C. D. Yes, the triangles are congruent by SSS. There is not enough information to determine if the triangles are congruent. No, the triangles are not congruent. Yes, the triangles are congruent by AAA. MAFS.912.G-CO.1.5 16. What are the coordinates of ′ if ′′′′ is a reflection of across the − ? A. B. C. D. (-5,-5) (-5,-1) (3,1) (5,1) MAFS.912.G-CO.3.10 17. If ∆ is an equilateral triangle and ∠ = 34°, what is ∠? A. B. C. D. 26° 19° 46° 86° ANSWER KEY Geometry Winter Review MAFS.912.G-CO.1.5 18. What is the rule for the transformation below? A. B. C. D. (′ , ′) (′ , ′) (′ , ′) (′ , ′) = = = = 2014-2015 (− − 6 , − + 1) ( − 6 , − + 1) ( − 6 , − 1) ( − 6 , + 1) MAFS.912.G-CO.1.5 19. Which of the following sequences of transformations will carry rectangle A onto rectangle B? A. B. C. D. Rotate rectangle A 90° counterclockwise about the origin, reflect it over the y-axis, and translate it 1 unit up. Translate rectangle A 7 units down, rotate it 180° about the point (2, -6), and translate it 8 units to the left. Reflect rectangle A over the x-axis, translate it 2 units up, and reflect it over the y-axis. Rotate rectangle A 90° clockwise about the origin, and translate it 2 units upand 6 units to the right. ANSWER KEY Geometry Winter Review MAFS.912.G-CO.2.8 20. Triangle is translated to create triangle . 2014-2015 Is triangle JKL congruent to triangle RST? A. B. C. D. Yes, the triangles are congruent by AAA. Yes, the triangles are congruent by SAS. There is not enough information to determine if the triangles are congruent. No, the triangles are not congruent. MAFS.912.G-CO.3.9 21. In the picture below, two lines intersect at point F. Angle AFC is represented by (9x)° and angle AFB is represented by (225 - 14x)°. Picture not drawn to scale What is the measure of BFD? A. B. C. D. 91° 90° 9° 81° MAFS.912.G-CO.3.9 22. Lines f and g are parallel lines cut by the transversal d. If the measure of ∠2 is 51°, what is the measure of ∠8? A. B. C. D. Picture not drawn to scale 129° 61° 51° 119° ANSWER KEY Geometry Winter Review MAFS.912.G-CO.1.1 23. Which of the following statements is the definition of parallel lines? A. B. C. D. 2014-2015 Two distinct coplanar lines that intersect at a 90°angle. Two distinct coplanar lines that do not intersect. Two rays with a common endpoint that point in opposite directions. Two rays sharing a common endpoint. MAFS.912.G-GPE.2.6 24. In the reflection of a polygon, which of the following characteristics of the polygon remain the same? A. B. C. D. I and III I and II I, II, III II and III MAFS.912.G-GPE.2.7 25. A triangle is shown on the coordinate plane below. What is the perimeter of the triangle? A. B. C. D. 10.63 units 25.63 units 28 units 56 units ANSWER KEY Geometry Winter Review 2014-2015 MAFS.912.G-SRT.1.1 26. Which of the following represents a polygon that is two times the size of the original polygon? A. B. C. D. MAFS.912.G-CO.3.10 27. Given isosceles trapezoid ABCD with ̅̅̅̅ ≅ ̅̅̅̅ and ∠ ≅ ∠, determine the missing reason to prove ∆ ≅ ∆. A. B. C. D. alternate exterior angles conjecture alternate interior angles conjecture vertical angle conjecture corresponding angles conjecture ANSWER KEY Geometry Winter Review 2014-2015 MAFS.912.G-CO.3.10 ̅̅̅̅ and point E is the midpoint of segment ̅̅̅̅ . 28. Given: Point D is the midpoint of ̅̅̅̅ ̅̅̅̅ ∥ Prove: Proof: Which of the following reasons complete the proof? A. B. C. D. Angle-Angle similarity postulate Triangle Midsegment Theorem Side-Angle-Side similarity theorem Side-Side-Side similarity theorem MAFS.912.G-SRT.1.1 29. If the scale factor of a dilation is less than one and greater than zero, what happens to the resulting image? A. B. C. D. The resulting image will be a rotation of the original image. The resulting image will be an enlargement of the original image. The resulting image will be a reduction of the original image. The resulting image will be a translation of the original image. ANSWER KEY Geometry Winter Review MAFS.912.G-CO.3.10 30. Complete this proof of the isosceles triangle theorem. Given: ∆ is isosceles Construct: ray BD bisecting ∠ Prove: ∠ ≅ ∠ A. B. C. D. SSS congruence SAS congruence AAS congruence SSA congruence ANSWER KEY 2014-2015