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MATH 1: Accelerated
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Final Exam Review (2015 – 2016) Unit 4 Transformations and Proofs GEOMETRY
Naming and Notation: Unions and Intersections: Given each geometric figure below, write the requested name using appropriate symbols and notation according to each union and intersection. 1. 𝐹𝐺⋂𝐼𝐺 = __________
2. 𝐹𝐺⋃𝐹𝐼 = __________
3. 𝐹𝐻⋃𝐻𝐽 = __________
4. 𝐹𝐻⋂𝐻𝐽 = __________
5. 𝐹𝐻⋃𝐻𝐹 = __________
6. 𝐹𝐻⋂𝐻𝐽 = __________
7. 𝐹𝐻⋃𝐻𝐼⋃𝐼𝐹 = __________
8. 𝐹𝐻⋂𝐻𝐼⋂𝐼𝐹 = __________
Sketch the following figures. Label all figures appropriately according to the name provided. 9. Acute ∡𝐸
10. Straight ∡𝐵𝐶𝐷 11. 𝐺𝐻
12. Right ∡𝐽𝐾𝐿 13. 𝐺𝐻 is the perpendicular bisector of 𝐴𝐵
14. ⊙ 𝑂 with diameter 𝐴𝐵
MATH 1: Accelerated
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Final Exam Review (2015 – 2016) Unit 4 Transformations and Proofs GEOMETRY
Sketch the following figures: 15. In the space to the right, draw two points. Label the
points A and B.
a. Draw the set of all points equidistant from A and B.
b. What is the name of the figure you drew in part a?
16. In the space to the right, draw one point. Label the
points C.
a. Draw the set of all points equidistant from C.
b. What is the name of the figure you drew in part a?
Solve for the indicated variable or measures. 17. If the 𝑚∡𝐴 = 61°, write the measure of its
complementary angle.
18. Given the angle below, write the measure of its supplementary angle.
19. If the measure of an angle is represented by 2𝑥:
a. Circle the expression below that represents the measure of its complement? (i) 180 – 2x (ii) 90 + 2x (iii) 90 – 2x (iv) 88x
b. Write an expression for the supplement of the angle. 20. Solve for 𝑎.
MATH 1: Accelerated
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Final Exam Review (2015 – 2016) Unit 4 Transformations and Proofs GEOMETRY
21. Solve for 𝑥.
22. Solve for 𝑥.
23. Sketch obtuse ∡𝐽𝐾𝐿.
a. Sketch in an angle bisector ray KM.
b. If 𝑚∡𝐽𝐾𝑀 = 72°,
then 𝑚∡𝐽𝐾𝐿 = __________________
24. 𝐴𝐵 and 𝐶𝐷 intersect at 𝐸. Sketch the figure.
If 𝑚∡𝐴𝐸𝐶 = 5𝑥 − 20 and 𝑚∡𝐵𝐸𝐷 = 𝑥 + 50 Then: 𝑚∡𝐶𝐸𝐵 =________________
25. The sum of the measures of angles 𝑥 and 𝑦 is 180°. The measure of angle 𝑥 is 24° greater than the measure of
angle 𝑦. a. Define the variables and write a system of equation for this situation b. Solve the system and find the measure of each angle.
MATH 1: Accelerated
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Final Exam Review (2015 – 2016) Unit 4 Transformations and Proofs GEOMETRY
26. Use what you know about angle relationships to set up a system of equations. Then solve for 𝒙 𝒂𝒏𝒅 𝒚.
27. Select the best answer to the multiple-‐choice questions below.
MATH 1: Accelerated
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Final Exam Review (2015 – 2016) Unit 4 Transformations and Proofs GEOMETRY
28.
𝑥 = _____________ 𝐹𝐻 = _____________
𝐹𝐺 = _____________
𝐻𝐺 = _____________
29.
𝑥 = _____________ 𝑚∡𝐴 = _____________
𝑚∡𝐵 = _____________
𝑚∡𝐶 = _____________
Write reason next to the appropriate statement in the right hand column. 30. Given: ∡𝐴𝐷𝐹 = 90°,∡𝐵𝐷𝐹 𝑖𝑠 𝑎 𝑟𝑖𝑔ℎ𝑡 𝑎𝑛𝑔𝑙𝑒
Prove: ∡𝐴𝐷𝐹 ≅ ∡𝐵𝐷𝐹
Statement Reason
1) ∡𝐵𝐷𝐹 𝑖𝑠 𝑎 𝑟𝑖𝑔ℎ𝑡 𝑎𝑛𝑔𝑙𝑒 1)
2) 𝑚∡𝐵𝐷𝐹 = 90° 2)
3) 𝑚∡𝐴𝐷𝐹 = 90° 3)
4) 𝑚∡𝐵𝐷𝐹 = 𝑚∡𝐴𝐷𝐹 4)
5) ∡𝐴𝐷𝐹 ≅ ∡𝐵𝐷𝐹 5)
x+15°
2x+45°
A C
B
MATH 1: Accelerated
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Final Exam Review (2015 – 2016) Unit 4 Transformations and Proofs GEOMETRY
31. Determine if the triangles are congruent.
• If so, write the theorem (SAS, ASA, SSS, AAS, HL) • If not, state “not congruent”.
a. __________________________
b. __________________________
c. __________________________
d. __________________________
e. __________________________
f. __________________________
g. __________________________
h. __________________________
i. __________________________
For each pair of triangles, determine
• Are they congruent • Write the triangle congruency statement • Give the postulate that makes them congruent. •
32. Given: T is the midpoint of 𝑊𝑅
a. Yes No
b. ∆__________________ ≅ ∆___________________
c. ______________________
33.
a. Yes No
b. ∆__________________ ≅ ∆___________________
c. ______________________
MATH 1: Accelerated
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Final Exam Review (2015 – 2016) Unit 4 Transformations and Proofs GEOMETRY
34. Given: I is the midpoint of 𝑀𝐸 and 𝑆𝐿
a. Yes No
b. ∆__________________ ≅ ∆___________________
c. ______________________
35. Given: 𝐵𝐷 bisects ∡𝐴𝐵𝐶
a. Yes No
b. ∆__________________ ≅ ∆___________________
c. ______________________
36. The two triangles below are congruent by Theorem ASA.
a. Which parts of the pair of triangles must be be shown congruent to satisfy ASA? __________________ ≅ ___________________
b. Write the congruence statement for the two triangles: ∆__________________ ≅ ∆___________________
MATH 1: Accelerated
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Final Exam Review (2015 – 2016) Unit 4 Transformations and Proofs GEOMETRY
37. Use the given information to mark the diagram. Then fill in the blank by writing the appropriate statement or
reason for each step of the two-‐column proof. Given: ∡𝑃 ≅ ∡𝑇 𝑅 𝑖𝑠 𝑡ℎ𝑒 𝑚𝑖𝑑𝑝𝑜𝑖𝑛𝑡 𝑜𝑓 𝑄𝑆 Prove: ∆𝑃𝑄𝑅 ≅ ∆𝑇𝑆𝑅
1) ∡𝑃 ≅ ∡𝑇
𝑅 𝑖𝑠 𝑡ℎ𝑒 𝑚𝑖𝑑𝑝𝑜𝑖𝑛𝑡 𝑜𝑓 𝑄𝑆
1)
2)
2) 𝐷𝑒𝑓𝑖𝑛𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑀𝑖𝑑𝑝𝑜𝑖𝑛𝑡
3)
3) 𝐷𝑒𝑓𝑖𝑛𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝐴𝑛𝑔𝑙𝑒𝑠 (𝐺𝑖𝑣𝑒𝑛 𝑖𝑛 𝑑𝑖𝑎𝑔𝑟𝑎𝑚)
4) ∡𝑃𝑅𝑄 ≅ ∡𝑇𝑅𝑆
4)
5) ∆𝑃𝑄𝑅 ≅ ∆𝑇𝑆𝑅
5)
MATH 1: Accelerated
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Final Exam Review (2015 – 2016) Unit 4 Transformations and Proofs GEOMETRY
38. Write Proofs for each problem below. Do these on a separate sheet of paper.
a.
b.
c.
Prove: 𝑀𝐿 ≅ 𝑂𝑁
d.
e.
△ 𝐸𝐷𝐶
MATH 1: Accelerated
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Final Exam Review (2015 – 2016) Unit 4 Transformations and Proofs GEOMETRY
f.
g.
f.
g.
Given: ∠ABC and ∠DBC areright angles, and DC≅AC
Prove: DBC≅ ABCD A
C
B
MATH 1: Accelerated
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Final Exam Review (2015 – 2016) Unit 4 Transformations and Proofs GEOMETRY
39. Find the measure of ∠ACB .
40. Find the value of x.
42. Find the value of a and b in the diagram below.
43. Find m∠j
2x°
5x°
65°B
D
C
A
2x°
5x°
65°B
D
C
A
