Geometry Midterm 1-5 STUDY GUIDE

Transcription

1 Geometry Midterm 1-5 STUDY GUIDE Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Is the line through points P( 7, 6) and Q(0, 9) parallel to the line through points R(0, 1) and S( 1, 3)? Explain. a. No, the lines have unequal slopes. b. Yes; the lines are both vertical. c. No, one line has slope, the other has no slope. d. Yes; the lines have equal slopes. 2. Is the line through points P( 7, 6) and Q( 5, 14) perpendicular to the line through points R(2, 10) and S(4, 2)? Explain. a. Yes; their slopes have product 1 b. Yes; their slopes are equal. c. No, their slopes are not reciprocals. d. Yes; their slopes have product 1 3. Based on the given information, what can you conclude, and why? Given: I K J H L a. by ASA c. by SAS b. by ASA d. by SAS 4. Name the theorem or postulate that lets you immediately conclude A B D C a. SAS b. ASA c. AAS d. none of these

2 5. Supply the missing reasons to complete the proof. Given: and Prove: I K J H L a. ASA; Substitution c. SAS; CPCTC b. AAS; CPCTC d. ASA; CPCTC 6. Which three lengths could be the lengths of the sides of a triangle? a. 19 cm, 7 cm, 8 cm c. 8 cm, 15 cm, 22 cm b. 14 cm, 7 cm, 21 cm d. 9 cm, 24 cm, 11 cm Short Answer 7. Find the distance between points P(7, 6) and Q(5, 8) to the nearest tenth. 8. Find the coordinates of the midpoint of the segment whose endpoints are H(4, 11) and K(2, 13). 9. Ralph wants to put a fence around his rectangular garden. His garden measures 39 feet by 53 feet. The garden has a path around it that is 3 feet wide. How much fencing material does Ralph need to enclose the garden and path? 10. Find the circumference of the circle to the nearest tenth.use 3.14 for. 25 m

3 11. Find the area of the circle in terms of. 44 in. 12. Find, to the nearest tenth, the area of the region that is inside the square and outside the circle. The circle has diameter 4 inches. 13. Supplementary angles are two angles whose measures have sum. Complementary angles are two angles whose measures have sum. 14. Find the values of x and y. 4y 2x Drawing not to scale 15. Line r is parallel to line t. Find m 5. The diagram is not to scale. r t

4 16. Find the value of the variable if and The diagram is not to scale l m 17. Find the value of x. The diagram is not to scale x 18. Find the value of the variable. The diagram is not to scale. 117 x Find. The diagram is not to scale A

5 20. The two triangles are congruent as suggested by their appearance. Find the value of c. The diagrams are not to scale. g 24 b 5 d 4 f 3 e 66 c 21. Justify the last two steps of the proof. Given: and Prove: M N O P Proof: Given Given From the information in the diagram, can you prove? Explain.

6 ( 23. Find the values of x and y. A y x 68 B D C Drawing not to scale 24. Use the information in the figure. Find E D 108 F Drawing not to scale 25. Find the value of x. The diagram is not to scale. 38 x

7 26. Q is equidistant from the sides of Find the value of x. The diagram is not to scale. T Q S (4x + 9) 29 R 27. Name a median for C F G ) ) E H D 28. Name the point of concurrency of the angle bisectors. 29. What is the name of the segment inside the large triangle?

8 ( ( 30. For the two quadrilaterals below, and Complete this congruence statement for the two quadrilaterals.? 31. Prove:. A D B C 32. Given: Prove: Q R P S

9 33. Given: is the perpendicular bisector of IK. Name two lengths that are equal. A I J K B 34. Find the values of x, y, and z. The diagram is not to scale x z y 35. List the sides in order from shortest to longest. The diagram is not to scale. J K 80 L 36. Write an equation for the line parallel to y = -2x + 15 that contains P(8, -6).

10 Other 37. Line p contains points A( 6, 1) and B(2, 4). Line q is parallel to line p. Line r is perpendicular to line q. What is the slope of line r? Explain. 38. T is the midpoint of QR. U is the midpoint of QS. RS = 36 and m QUT = 85. What are TU and m QSR? Explain. Q T U R S 39. Two sides of a triangle have lengths 6 and 8. What lengths are possible for the third side? Explain.

11 Geometry Midterm 1-5 STUDY GUIDE Answer Section MULTIPLE CHOICE 1. REF: 3-6 Slopes of Parallel and Perpendicular Lines TOP: 3-6 Example 1 2. REF: 3-6 Slopes of Parallel and Perpendicular Lines TOP: 3-6 Example 4 3. REF: 4-3 Triangle Congruence by ASA and AAS TOP: 4-3 Example 4 4. REF: 4-3 Triangle Congruence by ASA and AAS TOP: 4-3 Example 2 5. REF: 4-4 Using Congruent Triangles: CPCTC TOP: 4-4 Example 1 6. REF: 5-5 Inequalities in Triangles TOP: 5-5 Example 4 SHORT ANSWER 7. REF: 1-6 The Coordinate Plane TOP: 1-6 Example 1 8. REF: 1-6 The Coordinate Plane TOP: 1-6 Example 3 9. REF: 1-7 Perimeter, Circumference, and Area TOP: 1-7 Example REF: 1-7 Perimeter, Circumference, and Area TOP: 1-7 Example REF: 1-7 Perimeter, Circumference, and Area TOP: 1-7 Example REF: 1-7 Perimeter, Circumference, and Area TOP: 1-7 Example REF: 2-5 Proving Angles Congruent TOP: 2-5 Example REF: 2-5 Proving Angles Congruent TOP: 2-5 Example REF: 3-1 Properties of Parallel Lines TOP: 3-1 Example REF: 3-1 Properties of Parallel Lines TOP: 3-1 Example REF: 3-3 Parallel Lines and the Triangle Angle-Sum Theorem TOP: 3-3 Example REF: 3-3 Parallel Lines and the Triangle Angle-Sum Theorem 19. REF: 3-4 The Polygon Angle-Sum Theorems 20. REF: 4-1 Congruent Figures TOP: 4-1 Example REF: 4-2 Triangle Congruence by SSS and SAS TOP: 4-2 Example REF: 4-3 Triangle Congruence by ASA and AAS TOP: 4-3 Example REF: 4-5 Isosceles and Equilateral Triangles TOP: 4-5 Example REF: 4-5 Isosceles and Equilateral Triangles TOP: 4-5 Example REF: 5-1 Midsegments of Triangles TOP: 5-1 Example REF: 5-2 Bisectors in Triangles TOP: 5-2 Example REF: 5-3 Concurrent Lines, Medians, and Altitudes TOP: 5-3 Example REF: 5-3 Concurrent Lines, Medians, and Altitudes 29. REF: 5-3 Concurrent Lines, Medians, and Altitudes TOP: 5-3 Example REF: 4-1 Congruent Figures TOP: 4-1 Example REF: 4-4 Using Congruent Triangles: CPCTC TOP: 4-4 Example REF: 4-4 Using Congruent Triangles: CPCTC TOP: 4-4 Example REF: 5-2 Bisectors in Triangles TOP: 5-2 Example REF: 3-3 Parallel Lines and the Triangle Angle-Sum Theorem TOP: 3-3 Example REF: 5-5 Inequalities in Triangles TOP: 5-5 Example 3 36.

12 OTHER 37. REF: 3-6 Slopes of Parallel and Perpendicular Lines 38. REF: 5-1 Midsegments of Triangles 39. REF: 5-5 Inequalities in Triangles