Geometry Essentials (2015-2016) Midterm Review Name: Chapter 1 For numbers 1 4, use the diagram below. 1. Classify as acute, obtuse, right or straight. 2. is a linear pair with what other angle? 3. Name an angle adjacent to. 4. Name an angle vertical to. 5. Find the value of x using the diagram below. 6. Two angles are complementary. The first angle measures 15 and the second angle measures 14. Find the measure of the second angle. Chapter 2 State the definition, property, postulate, or theorem that justifies each statement. 7. If X is the midpoint of, then. 8. If K P and P T, then K T. 9. If m W + m H = 90 and m H = 20, then m W + 20 = 90. 10. If A and B are complementary, then m A + m B = 90. 11. If then AT = DR. 12. AB + BC = AC
Chapter 3 13. Find the slope of a line that is perpendicular to. 14. Write an equation in slope-intercept form for the line that passes through the point 1, 4 and is parallel to the linear graph of 2 5. For numbers 15 17, use the diagram to the right. 15. Name the relationship between angles 8 and 14 and tell whether they are congruent or supplementary. 16. Name the relationship between angles 5 and 13 and tell whether they are congruent or supplementary. 17. Name the relationship between angles 7 and 14 and tell whether they are congruent or supplementary. 18. Find the value of x. 19. Find the value of x.
Chapter 4 20. Triangles ABC and PQR are congruent. Which statement about the triangles is true? a) A R b) C R c) AB RQ d) CB PQ 21. Which figure contains two congruent triangles? a) b) c) d) 22. Triangle ABC is congruent to triangle XYZ, as shown below. Which of the following statements must be true? a) m X = 45 b) m Z = 45 c)yz 3 cm d) XY 3 cm 23. If EFG HIJ, which of the following statements must be true? a) EFG JIH b) EFG IJH c) FEG IHJ d) FGE HIJ 24. Consider these statements. *No equilateral triangles are obtuse. *Triangle KJF is obtuse. Which conclusion can be made using both statements? a) Triangle KJF is scalene. b) Triangle KJF is not isosoceles. c) Triangle KJF is a right triangle. d) Triangle KJF is not equiangular.
25. Jeremy is proving the following theorem: If two angles are congruent to two angles of a second triangle, then the third angles of the triangles are congruent. Jeremy s proof is shown below. Given: Q T P S Prove: R V Statements Reasons 1. Q T 1. Given P S 2. m Q = m T 2. Definition of Congruency m P = m S 3. m P + m Q + m R = 180 3. The interior angles of a triangle add to 180 m S + m T + m V = 180 4. m P + m Q + m R = m S + m T + m V 4. Transitive Property of Equality 5.? 5. Substitution Property 6. m R = m V 6. Subtraction Property of Equality 7. R V 7. Definition of Congruency Which statement BEST represents Step 5 of Jeremy s proof? a) 180 = 180 b) 180 m R = 180 m V c) m P + m Q = m T + m S d) m P + m Q + m R = m P + m Q + m V 26. Manuel is trying to prove the following theorem. If two sides of a triangle are congruent, then the angles opposite these sides are congruent. First Manuel draws isosceles PQR, and then he adds an auxiliary line that bisects PQR. Q An incomplete version of Manuel s proof is shown below. Statements Reasons 1. PQ = RQ 1. Given 2. m PQS = m RQS 2. QS bisects PQR 3. QS = QS 3. Reflexive Property 4.? 4. 5. m QPS = m QRS 5. P S R What should be the statement for Step 4 of Manuel s proof? a) PQR is a right angle b) PQS RQS c) PSQ RSQ d)ps SR
27. The statements for a proof are shown. Statements Reasons 1. Parallelogram ABCD 1. Given 1 2 2. B D 2. 3. AB DC 3. 4. ABX CDY 4. 5. BX DY 5. What is the reason that the statement in Step 5 is true? a) angle-side-angle b) side-angle-side c) Opposite sides of a parallelogram are congruent d) Corresponding parts of congruent triangles are congruent (CPCTC) 28. A triangle is shown. Which triangle is congruent to this triangle? a) b) c) d) 29. Triangle EFG is congruent to Triangle HIJ. What is the measure of Angle IJH? a) 24 b) 80 c) 156 d) 204 30. Triangles ADC and BCD are shown below. What additional fact is needed to prove ADC BCD by the htpotenuse leg theorem? a) A B b) AC BD c) AD BC d) m A = m B = 45
31. In the figure below, XYZ XWZ. What is the length of XY? a) 7 b) 9 c) 10 d) 12 32. In the figure to the right, QR SR and PR TR. Based only on the given information, which theorem could be used to prove PQR TSR? a) Side-Side-Side b) Side-Angle-Side c) Side-Side-Angle d) Angle-Side-Angle 33. If OMR STP, which relationship must be true. a) RM TS b) RO PS c) MRO PST d) RMO TPS 34. In the figure shown, M T, and R is the midpoint of MT. To prove MN TP, a student wrote the following 6 statements. 1. M T 2. R is the midpoint of MT 3. MR = TR 4. MRN TRP 5. MRN TRP 6. MN TP Which reason should the student give for statement 5? a) Side-Angle-Side b) Side-Angle-Angle c) Angle-Side-Angle d) Angle-Angle-Angle
35. A proof is shown below. Given: LM PQ and MT TP Prove: LMT QPT STATEMENT REASON 1. LM PQ and MT TP 1. Given 2. MLT PQT 2. Alternate Interior Angles Theorem 3. LTM QTP 3. 4. LMT QTP 4. Angle-Side-Angle Theorem Which reason is justification for statement 3? a) Angle Bisector Theorem b) Vertical Angles Theorem c) definition of congruent angles d) definition of congruent triangles 36. In the figure below, PQ RQ and PS RS. Based only on the given information, which theorem could be used to prove PQS RQS? a) Side-Side-Side b) Side-Side-Angle c) Side-Angle-Side d) Angle-Side-Angle 37. ABC is shown. Which value of x will prove ABC is a right triangle? a) x = 10 b) x = 30 c) x = 45 d) x = 91 A (3x) (2x + 1) B C (x 1) 38. Which statement describes a triangle that must be scalene? a) A triangle with all sides congruent. b) A triangle with all angles congruent. c) A triangle with 2 sides congruent. d) A triangle with no sides congruent. 39. Which statement is NOT enough information to prove the two triangles shown are congruent? a) A D and B E b) AC DFand A D c) AC DF and AB DE d) AC DFand B E
40. Which expression represents the missing x-coordinate for S? a) 3b b) 0 3 b 2 c) 0 3b d) cannot be determined 41. XY is the hypotenuse of right XYZ. Which of the following could be the coordinates of Z? a) (0, 0) b) ( 2, 2) c) ( 1, 2) d) (0, 2)