Geometry Midterm - Study Guide
1. M(-2,4) is the midpoint of RS . If S has the coordinates (4, -2) find the coordinates of R .
2. In the figure shown, IM bisects ∠ HIJ . Identify the two congruent angles created by the bisection.
H
M
L
K
I J
3. Draw a hexagon.
4. Determine whether the figure below is a polygon. If it is not a polygon, explain why.
5. What name is given to polygons whose sides all have the same length and whose angles all have the same measure?
6. How many diagonals can be drawn from one vertex of a regular decagon?
7. If quadrilateral ABCD is congruent to quadrilateral UVWX , then BC is congruent to .

[A]
[B]
41
40
8
9
[C]
[D]
9
8
40
41
Geometry Midterm - Study Guide
8. ∆ ABC ≅
N M C
P A B
[A] ∆ MNP
[B] ∆ NMP
[C] ∆ NPM
[D] ∆ CAB
9. Castro is planting a circular garden. The garden is divided into equal sections. Each section has a central angle of 90 ° . How many sections are there?
10. Find the missing elements in the sequence below.
2, 4, 8, 14, 22, 32 , , 112, . . .
11. If the pattern were continued, what would be the ratio of the number of unshaded squares to the number of shaded squares in the next figure in the pattern?

Geometry Midterm - Study Guide
12. A number is divisible by 6 if the sum of the digits of the number is divisible by 3 and the number is even. Using deductive reasoning, what conclusion can be made about 156,084?
13. Three girls are in three different rooms. Sally always tells the truth. Naomi sometimes tells the truth. Julia never tells the truth. Use the statements made by the person in each room to tell who is in each of the rooms.
[A] Room 1 - Sally; Room 2 - Julia; Room 3 - Naomi
[B] Room 1 - Naomi; Room 2 - Julia; Room 3 - Sally
[C] Room 1 - Julia; Room 2 - Sally; Room 3 - Naomi
[D] Room 1 - Julia; Room 2 - Naomi; Room 3 - Sally
14. Find the values of x and y . x y
115°
15. In the figure, l II m and j II k Name all angles congruent to ∠ 8. l m j
1 2
5 6
3 4
7 8
9 10 11 12
13 14 15 16 k

Geometry Midterm - Study Guide
16. Find the unknown angle measures, given that lines l and m are parallel. m
93°
72° d a e
37° b c
56° l
17. Find x . b x + 7 ° g f
A b
4 x − 8 ° g
18. Find the slope of the line containing the points A b g
and B b
9 10 g
.
19. Find AB if AC = 28 centimeters and the perimeter of triangle ABC is 52 centimeters.
B
D
C
20. Is AD an angle bisector of ∠ BAC ?
B
D
10 ft
9 ft
A C
21. Given a 60 ° angle, describe how you would construct a 30 ° angle using only a compass and straightedge.

Geometry Midterm - Study Guide
22. Which shows the construction of the line parallel to line j and through point K ?
K j
[A]
K j
[B]
K j
[C] j
K
[D] j
K

Geometry Midterm - Study Guide
Use only a compass and straightedge to complete the following constructions.
23. Construct a rectangle with sides of lengths a and b . a b
24. Construct the circumcenter of ∆ JKL .
K
L
J
25. If the three altitudes of a triangle are constructed, which point of concurrency is created?
[A] incenter
[B] circumcenter
[C] center
[D] orthocenter
26. If point P is the incenter and the combined length of segments JP , KP , and LP is 12 centimeters, what is the length of segment JP ?
B
A
J
P
K
L
C

Geometry Midterm - Study Guide
27. The centroid of a triangle divides each median into two parts so that the distance from the centroid to the vertex is _____ the distance from the centroid to the midpoint of the opposite side.
28. Point P is the centroid of the triangle shown below. If BL is 15 centimeters, what is PL ?
B
K
J
P
C
L
A
[A] 5.0 cm
[B] 15.0 cm
[C] 7.5 cm
[D] 45.0 cm
29. Find x given that ∠ PQR ≅ ∠ PRQ .
P b x + 8 g
m
17 m
Q R
30. Tell whether it is possible to construct a triangle with the given sides lengths.
2
1
2
in., 4
1
2
in., 7
1
2
in.

Geometry Midterm - Study Guide
31. Tell whether ∆ ABC and ∆ DEC are congruent. Explain how you know.
E D
6 in.
10 in.
10 in.
C
6 in.
A B
32. Refer to the figure and information given below. Give a congruence statement for two triangles in the figure and name the congruence conjecture that supports the congruence.
H
G J I
GJ ≅ JI
33. Determine what information you would need to know in order to use the SSS Congruence
Conjecture to show that the triangles are congruent.
B
A
C
D
[A] ∠ BAD ≅ ∠ CDB
[B] AD ≅ BD
[C] ∠ ADB ≅ ∠ CBD
[D] AD ≅ CB

Geometry Midterm - Study Guide
34. If ∆ BCD ≅ ∆ EFG , what six things can you conclude about the corresponding parts of the two triangles?
35. If BCDE is congruent to TUVW , then CD is congruent to which segment in TUVW ?
[A] UV
[B] TU
[C] TW
[D] UW
36. Find the value of x so that ∆ ABC ≅ ∆ XYZ . m A = 46 , BC = b
7 x + 3 g
meters, m X = ° AC = 31 meters, YZ = b
6 x + 6 g
meters
A Z Y
B C X
[A] x = 6
[B] x = 5
[C] x = 3
[D] x = 4
37. If ∆ ABC ≅ ∆ DEF , AB = 11 centimeters, ∠ ABC = ° ∠ DFE = ° following statements cannot be shown to be true?
[A] ∠ CAB °
[B] FD = 11 cm
[C] BC ≅ EF
[D] ∠ D ≅ ∠ A

Geometry Midterm - Study Guide
38. DE is a median and altitude of ∆ GDF . What is the measure of angle DFE ?
D
G
41 °
E
F
[A] 41 degrees
[B] 90 degrees
[C] 39 degrees
[D] 180 degrees
39. What can you conclude about ∆ EGF ?
40. Find m L .
K
6 cm 6 cm
J
6 cm
L

Geometry Midterm - Study Guide b
5 g
[2] ∠ HIM and ∠ JIM
[3] Sample drawing:
[4] The figure is a polygon.
[5] regular polygons
[6] 7
[7] VW
[8] [A]
[9] 4 sections
[10] 44, 92
[11] [A]
[12] Because the sum of the digits in 156,084 equal 24, and the number is even, 156,084 is divisible by 6.
[13] [D]
[14] x = 115 ° ; y = 65 °

Geometry Midterm - Study Guide
[15] angles 1, 3, 6, 9, 11, 14, 16
[16] a = ° b = ° c = ° d = ° e = ° f = 37
[17] x = 5
[18]
1
3
[19] AB = 12 cm
[20] No
[21] Bisect the angle.
[22] [A]
[23]
[24] Sample answer:

Geometry Midterm - Study Guide
K
L
J
[25] [D]
[26] JP = 4 cm
[27] twice
[28] [A]
[29] 9 m
[30] No
[31] Yes. SAS
[32] ∆ GHJ ≅ ∆ IHJ by the SAS Conjecture
[33] [D]
[34] BC ≅ , ≅ , ≅ E G , ∠ B ≅ ∠ E , ∠ C ≅ ∠ F , ∠ D ≅ ∠ G
[35] [A]
[36] [C]
[37] [B]

Geometry Midterm - Study Guide
[38] [A]
[39] ∆ EGF is equilateral and equiangular.
[40] 60 °