Name: ________________________ Period: ___________________ Date: __________
GeoBM3Review2011 1. DE and CF ____ be coplanar. a. must b.
may
c.
cannot
2. Name the line and plane shown in the diagram.
← →
a.
RS and plane RSU
← →
c.
RS and plane U R ← →
b.
line R and plane RSU
d.
SR and plane UT
4. Name an angle supplementary to ∠EOD.
3. If T is the midpoint of SU , find the values of x and ST. The diagram is not to scale.
a. b. c. d.
x = 5, ST = 45 x = 5, ST = 60 x = 10, ST = 60 x = 10, ST = 45
a. b. c. d.
1
∠BOC ∠BOE ∠DOC ∠BOA
ID: A
Name: ________________________
ID: A
5. ∠DFG and ∠JKL are complementary angles. m∠DFG = x + 5 , and m∠JKL = x − 9 . Find the measure of each angle. a. ∠DFG = 47, ∠JKL = 53 b. ∠DFG = 47, ∠JKL = 43 c. ∠DFG = 52, ∠JKL = 48 d. ∠DFG = 52, ∠JKL = 38
10. The Polygon Angle-Sum Theorem states: The sum of the measures of the angles of an n-gon is ____. n−2 a. 180 b. (n − 1)180 180 c. n−1 d. (n − 2)180
6. ∠1 and ∠2 are supplementary angles. m∠1 = x − 39, and m∠2 = x + 61. Find the measure of each angle. a. ∠1 = 79, ∠2 = 101 b. ∠1 = 40, ∠2 = 140 c. ∠1 = 40, ∠2 = 150 d. ∠1 = 79, ∠2 = 111
11. Complete this statement. The sum of the measures of the exterior angles of an n-gon, one at each vertex, is ____. a. (n – 2)180 b. 360 (n − 2)180 c. n d. 180n
7. Find the distance between points P(8, 2) and Q(3, 8) to the nearest tenth. a. 11 b. 7.8 c. 61 d. 14.9
12. Find the value of the variable if m Ä l, m∠1 = 2x + 44 and m∠5 = 5x + 38. The diagram is not to scale.
8. Find the coordinates of the midpoint of the segment whose endpoints are H(8, 2) and K(6, 10). a. (7, 6) b. (1, 4) c. (14, 12) d. (2, 8) a. b. c. d.
9. M(9, 8) is the midpoint of RS . The coordinates of S are (10, 10). What are the coordinates of R? a. (9.5, 9) b. (11, 12) c. (18, 16) d. (8, 6)
2
1 2 3 –2
Name: ________________________
ID: A
13. Find m∠Q. The diagram is not to scale.
a. b. c. d.
15. The folding chair has different settings that change the angles formed by its parts. Suppose m∠2 is 26 and m∠3 is 70. Find m∠1. The diagram is not to scale.
60 120 110 70
a. b. c. d.
96 106 116 86
14. Find the value of x. The diagram is not to scale. 16. Find the sum of the measures of the angles of the figure.
a. b. c. d.
33 162 147 75
a. b. c. d.
540 180 360 900
17. How many sides does a regular polygon have if each exterior angle measures 20? a. 17 sides b. 20 sides c. 21 sides d. 18 sides
3
Name: ________________________
ID: A
18. What is the missing reason in the two-column proof? →
→
Given: AC bisects ∠DAB and CA bisects ∠DCB Prove: ∆DAC ≅ ∆BAC
Statements
Reasons
→
1. AC bisects ∠DAB 2. ∠DAC ≅ ∠BAC 3. AC ≅ AC
1. Given 2. Definition of angle bisector 3. Reflexive property
→
4. CA bisects ∠DCB 5. ∠DCA ≅ ∠BCA 6. ∆DAC ≅ ∆BAC a. b.
4. Given 5. Definition of angle bisector 6. ?
ASA Postulate SSS Postulate
c. d.
SAS Postulate AAS Theorem
19. Explain how you can use SSS, SAS, ASA, or AAS with CPCTC to complete a proof. Given: CB ≅ CD, ∠BCA ≅ ∠DCA Prove: BA ≅ DA
4
Name: ________________________
ID: A 24. Two sides of a triangle have lengths 10 and 15. What must be true about the length of the third side, x? a. 5 < x < 25 b. 5 < x < 10 c. 5 < x < 15 d. 10 < x < 15
20. Find the value of x.
25. LMNO is a parallelogram. If NM = x + 15 and OL = 3x + 5 find the value of x and then find NM and OL. a. b. c. d.
4 8 6.6 6
a. b. c. d.
21. Which three lengths could be the lengths of the sides of a triangle? a. 12 cm, 5 cm, 17 cm b. 10 cm, 15 cm, 24 cm c. 9 cm, 22 cm, 11 cm d. 21 cm, 7 cm, 6 cm
x = 7, NM = 20, OL = 22 x = 5, NM = 20, OL = 20 x = 7, NM = 22, OL = 22 x = 5, NM = 22, OL = 20
26. DEFG is a rectangle. DF = 5x – 5 and EG = x + 11. Find the value of x and the length of each diagonal. a. x = 4, DF = 13, EG = 13 b. x = 4, DF = 15, EG = 18 c. x = 4, DF = 15, EG = 15 d. x = 2, DF = 13, EG = 13
22. Which three lengths can NOT be the lengths of the sides of a triangle? a. 23 m, 17 m, 14 m b. 11 m, 11 m, 12 m c. 5 m, 7 m, 8 m d. 21 m, 6 m, 10 m
23. Two sides of a triangle have lengths 10 and 18. Which inequalities describe the values that possible lengths for the third side? a. x ≥ 8 and x ≤ 28 b. x > 8 and x < 28 c. x > 10 and x < 18 d. x ≥ 10 and x ≤ 18
5
Name: ________________________
ID: A
27. For the parallelogram, find coordinates for P without using any new variables.
a. b. c. d.
(a – c, c) (c, a) (a + c, b) (c, b)
28. Find x, given that PQ Ä BC .
a. b. c. d.
12 6 20 24
6
ID: A
GeoBM3Review2011 Answer Section 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.
REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF:
1-3 Points, Lines, and Planes TOP: 1-4 Example 2 1-3 Points, Lines, and Planes 1-5 Measuring Segments TOP: 1-5 Example 3 1-6 Measuring Angles TOP: 1-6 Example 4 1-6 Measuring Angles 1-6 Measuring Angles 1-8 The Coordinate Plane TOP: 1-8 Example 1 1-8 The Coordinate Plane TOP: 1-8 Example 3 1-8 The Coordinate Plane TOP: 1-8 Example 4 3-5 The Polygon Angle-Sum Theorems 3-5 The Polygon Angle-Sum Theorems 3-1 Properties of Parallel Lines TOP: 3-1 Example 5 3-1 Properties of Parallel Lines 3-4 Parallel Lines and the Triangle Angle-Sum Theorem TOP: 3-4 Parallel Lines and the Triangle Angle-Sum Theorem TOP: 3-5 The Polygon Angle-Sum Theorems TOP: 3-5 The Polygon Angle-Sum Theorems TOP: 4-3 Triangle Congruence by ASA and AAS TOP: 4-4 Using Congruent Triangles: CPCTC TOP: 5-1 Midsegments of Triangles 5-5 Inequalities in Triangles TOP: 5-5 Example 4 5-5 Inequalities in Triangles TOP: 5-5 Example 4 5-5 Inequalities in Triangles TOP: 5-5 Example 5 5-5 Inequalities in Triangles TOP: 5-5 Example 5 6-2 Properties of Parallelograms TOP: 6-2 Example 2 6-4 Special Parallelograms TOP: 6-4 Example 2 6-6 Placing Figures in the Coordinate Plane TOP: 7-5 Proportions in Triangles TOP: 7-5 Example 1
1
3-4 Example 3 3-4 Example 4 3-5 Example 3 3-5 Example 3 4-3 Example 4 4-4 Example 2
6-6 Example 2
