Geometry Essentials
Midterm Review ANSWER KEY
Chapter 1
1. Obtuse
2.

AOD or

BOC
3.

EOD
4.

COD
5.
6. x x
= 6
= 5
(It is an angle larger than 90

)
(linear pairs need to have a common side, whose non common sides form a straight line)
(adjacent angles need to have a common side, but cannot overlap)
(vertical angles are across from each other and form a perfect X shape)
(Use Segment Addition to set up and solve: 4x + 24 = 7x + 6)
(Use Def. of Complementary Angles (they add to 90

) to set up and solve: x + 15 + 14x = 90)
Chapter 2 (reference your purple packet of proof patterns)
7. Midpoint Theorem
8. Transitive Property
9. Substitution
10. Definition of Complementary
11. Definition of Congruent Segments
12. Segment Addition
Chapter 3
13.
1
4
(Use 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛
to find the slope of the given line. This slope is −
4
1
. Perpendicular lines have opposite reciprocal slopes .)
14. y = –2 x + 2 (parallel lines have the same slope, so use m = –2 in point slope form y – y
1
= m(x – x
1
) . Distribute and get y alone.)
15. Alternate Interiror Angles; they are congruent
16. Corresponding Angles; they are congruent
17. Consecutive Interior Angles; they are supplementary
18. x = 17
19. x = 35
(Alternate Interior Angles are congruent so set up and solve: 4x – 10 = 58)
(Consecutive Interior Angles are supplementary so set up and solve: 2x + 43 + 2x – 3 = 180)
Chapter 4
20. B
21. A
22. A
23. C
(use the congruent statement to find the congruent parts)
(use reflexive property)
(use the congruent statement to fill in congruent angles, then use the ∆ sum rule, that all three angles add to 180

)
(check that corresponding angles are in the same location in each statement)
24. D
25. D
26. B
27. D
28. A
29. A (use the congruent statement to fill in congruent angles, then use the ∆ sum rule, that all three angles add to 180

)
30. B
31. C
32. B
33. B
34. C
35. B
36. A
37. B
38. D
39. A
(use reflexive property to mark 𝐷𝐶 , which is a leg (L), name each hypotenuse for H )
(Set corresponding sides equal to solve: 2x – 6 = 12, so x = 9. Substitute 9 back into XW since XW = XY )
(use vertical angles)
(draw triangles and use the congruent statement to find congruent corresponding parts)
(mark all of the congruent pieces in the picture)
(find the angles in statement 3. They are vertical angles)
(use reflexive property)
(Set the largest angle equal to 90

and solve for x: 3x = 90)
40. B
41. C
(mark each option, one at a time. Option B shows ASA; Option C shows HL, Option D shows AAS)
(use the midpoint formula since S is exactly halfway between J and R ) ( 𝑥
1
+𝑥
2
2
(draw 2 legs straight down and straight right. Z is where these legs intersect)
, 𝑦
1
+𝑦
2 )
2