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Geometry A Final Exam 2014-15 (Geometry A - TOR: AAI) 1. If angle EAC is congruent to angle ECA, name the congruent segments. A. AE, EC B. EC, CA C. AE, AC D. AE, EC, AC 2. Which of the following polygons is convex? A. B. C. D. 1 3. Triangle ABC =~ Triangle DFE. find the value of x. A. 8.54 B. 9.8 C. 12.92 D. 21.92 4. Name the polygon by its number of side. A. pentagon B. nonagon C. decagon D. dodecagon 5. Verify that quadrilateral BCDE is a rhombus with vertices B(-5, 1), C(0, 6), D(5, 1) and E (0, -4) by showing that all four sides are equal. A. BD = CE = B. BD = CE = 50 C. BC = CD = DE = EB = 50 D. BC = CD = DE = EB = 6. Find the value of x and y in parallelogram LMNP. A. x = 31, y = 2 B. x = -3, y = 2 C. x = 2, y = 31 D. x = 124, y = 10 7. WXYZ is a kite. If the measure of angle WXY is 120°, the measure of angle WZY is 4x° and the measure of angle ZWX is 10x°, find the measure of angle ZYX. A. 100° B. 171.43° C. 40° D. 80° 8. If the perimeter of a square is 64 cm, find the area. A. 32 cm2 B. 48 cm2 C. 64 cm2 D. 256 cm2 9. Which property states that if , then ? A. Reflexive B. Transitive C. Symmetric D. Multiplicative identity 10. If ABCD is a parallelogram, identify the two pairs of congruent segments. A. B. C. D. 11. Use the figure below to determine the relationship between the lengths of Click Here for a long description of the image above. A. = B. > C. < D. No relationship can be determined. and 12. Find the value of y in the rhombus below. A. 15 B. 120 C. 60 D. 30 13. Select the statement that rewrites the following definition as a conditional statement. Collinear points: points that lie on the same line. A. Points that lie on the same line are collinear B. If points lie on the same line, then they are collinear. C. If points are not collinear, then they do not lie on the same line D. Collinear points lie on the same line 14. Find the value of x. A. 80 B. 69 C. 31 D. 21 15. Classify the figure in as many ways as possible. A. rectangle, trapezoid, quadrilateral, parallelogram, rhombus B. rectangle, square, quadrilateral, parallelogram, rhombus C. rectangle, quadrilateral, parallelogram D. rhombus, trapezoid, quadrilateral, parallelogram 16. Which of the following could not be a value of n? A. 7 B. 10 C. 13 D. 22 17. What is the area of a triangle with a base of 20.3 m and a height of 5.6 m? A. 28.42 m2 B. 56.84 m2 C. 113.68 m2 D. 227.36 m2 18. What additional information is needed to conclude that the triangles are congruent by the side-side-side congruence postulate? A. O is the midpoint of PM. B. MO≅OP C. ON≅NO and MO≅OP D. No additional information is needed to show that the triangles are congruent by SSS. 19. Quadrilateral ABCD is a rectangle. The measure of angle CBE is equal to 32º, find the measure of angle CEB. A. 58° B. 74° C. 148° D. 116° 20. Find the area of the parallelogram. A. 69 cm2 B. 345 cm2 C. 276 cm2 D. 180 cm2 21. Find the value of a. A. 23.3 B. 16 C. 8 D. 64 22. IfΔXYZ≅ΔMNL , what is A. ∠L B. ∠M C. ∠N D. ∠Y ∠X congruent to? 23. What additional information is needed to verify that the triangles are congruent by the side-angle-side congruence postulate? A. ∠Y≅∠Z B. ∠XAY≅∠ZAX C. YA≅AZ D. No additional information is needed to show that the triangles are congruent by SAS. 24. Which of following is NOT a regular polygon? A. B. C. D. 25. The centroid of a triangle is the intersection of the A. altitudes B. medians C. angle bisectors D. perpendicular bisectors 26. The sum of the exterior angles of a convex polygon, one angle at each vertex, is equal to how many degrees? A. 90° B. 180° C. 360° D. 540° 27. The perimeter of a kite is 52 meters. If one side measures 19 meters find the measure of the opposite side. A. 16.5 meters B. 14 meters C. 7 meters D. 19 meters 28. If A. 2 , find x. B. 4 C. 6 D. Cannot be determined 29. State whether the following uses inductive or deductive reasoning: 1, 3, 5, 7,… The next number is 9. A. Inductive B. Deductive 30. WXYZ is an isosceles trapezoid. WY = 8a – 3 and ZX = 19. Find the value of a. A. 2 B. 2.375 C. 3.75 D. 2.75 31. Find the area of the kite. A. 54 cm2 B. 72 cm2 C. 108 cm2 D. 39 cm2 32. What is the 7th number in the pattern: 1, 4, 9, 16, 25, …? A. 32 B. 36 C. 39 D. 49 33. The orthocenter of a triangle is formed by the ____________of a triangle. A. perpendicular bisectors B. angle bisectors C. medians D. altitudes 34. Which statement can you use to conclude that quadrilateral XYZW is a parallelogram? A. and B. and C. and D. and 35. Which angle has the greater measure? A. ∠B B. ∠E C. ∠D D. The angles are congruent 36. If the area of a square is 1444 ft2, find the perimeter. A. 152 ft B. 288 ft C. 361 ft D. 304 ft 37. What additional information is needed in order to know that the triangles are congruent by the angle angle side congruence postulate. A. ∠XAY≅∠ZAX B. AY≅AZ C. No additional information is needed to show that the triangles are congruent by AAS. D. ∠Y≅∠Z 38. Given: and Prove: Complete the proof by choosing the correct statement for line number 4 and the correct reason for line number 6. Statement Reason 1. Given 2. 3. and interior angles 4. Given are alternate Definition of alternate interior angles Alternate Interior Angle Theorem Reflexive 5. 6. A. ; SAS B. ; SAS C. ; SSA D. ; SAS 39. DEFG is a parallelogram. Segment DH = y + 4, segment HF = 3x – 1, segment HE = 3x + 2 and segment GE = 28. Find the values of x and y. A. x = 4; y = 7 B. x= ; y = 21 C. x = 4; y = 11 D. x = 5; y = 12 40. Classify the triangle based on side lengths 4.5, 20 and 20.5. A. right B. acute C. obtuse D. no triangle can be formed with given side lengths 41. A 20 foot ladder is placed against a building to reach a window that is 16 feet above the ground. How many feet away from the building is the bottom of the ladder? A. 3 B. 4 C. 12 D. 15 42. What is the sum of the interior angles of a convex nonagon? A. 1620° B. 1800° C. 1260° D. 3240° 43. Find the perimeter of the polygon. A. 69 cm B. 425 cm C. 69 cm2 D. 425 cm2 44. Side one of a triangle is (3x+10), side two of a triangle is (5x) and side 3 of a triangle is (2x + 25). If the perimeter of the triangle is 200, find the value of x A. 16.5 B. 59.5 C. 82.5 D. 58 45. The HL congruence postulate applies to A. all triangles B. acute triangles C. right triangles D. obtuse triangles 46. Find the perimeter of an equilateral triangle with side length of 12 inches. A. 12 in B. 72 in C. 48 in D. 36 in 47. The diagram below shows the construction of the center of the circle circumscribed about △WXY. This construction represents how to find the intersection of A. the angle bisectors of △WXY B. the medians to the sides of △WXY C. the altitudes to the sides of △WXY D. the perpendicular bisectors of the sides of △WXY 48. In ABC below, BD is an altitude and D is the midpoint of AC. Are the triangles congruent? If they are congruent, write a congruence statement. A. ΔABD≅ΔCBD B. ΔABD≅ΔBDC C. ΔABD≅ΔCDB D. The triangles are not congruent. 49. Based on the two-column proof below, the SAS congruence postulate is the reason for what statement? Statements Reasons F is the midpoint of EG¯¯¯¯¯¯. F is the midpoint of HD¯¯¯¯¯¯. Given DF¯¯¯¯¯¯≅FH¯¯¯¯¯¯EF¯¯¯¯¯≅FG¯¯¯¯¯ Definition of midpoint Vertical angles are congruent. ∠DFE≅∠GFH SAS congruence postulate ΔDFE≅ΔHFG A. ∠DFE≅∠GFH B. ΔDFE≅ΔHFG C. EF¯¯¯¯¯≅FG¯¯¯¯¯ D. F is the midpoint of EG¯¯¯¯¯ 50. The sum of the measures of the angles of a triangle is ______. A. 90° B. 180° C. 270° D. 360°