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2016 - 2017
Honors Geometry
Midterm Study Guide
Name: _____________________________
Pd: _____
Due Date:________________
WORK MUST BE SHOWN TO
RECEIVE CREDIT
1. In the figure,
,
and
T
P
K
. Find the measure of angle RSM.
R
L
N
Q
M
S
U
2. Which segment is the shortest possible distance from point D to plane P?
D
S
U
T
Q
R
V
P
Given the following information, determine which lines, if any, are parallel. State the postulate or theorem that justifies your
answer.
c
10
d
3.
9
2
1
4
a
11
3
5
b
6
8
7
Write an equation in slope-intercept form of the line having the given slope and y-intercept.
2
4. − 3 and (-6, 4)
Complete the statement about parallelogram ABCD and explain why.
A
5.
B
G
6.
D
C
Determine whether the given measures can be the lengths of the sides of a triangle. Write yes or no. Explain.
7. 9.2, 11.6, 24.4
8. Find the measure of each exterior angle for a regular pentagon. Round to the nearest tenth if necessary.
In the figure,
and
are opposite rays.
and
9. If 𝑚∠𝐽𝐾𝑀 = 7𝑥 + 18 and 𝑚∠4 = 2𝑥, what is
bisects
.
?
J
P
1
K
2
3 4
N
L
10. Why is ∠3 ≅ ∠4?
11. If 𝑚∠𝐿𝐾𝑁 = 9𝑥 − 4 and 𝑚∠4 = 6𝑥 + 10, what is
?
12. Triangles ABC and AFD are vertical congruent equilateral triangles. Find x and y.
B
C
(2 y+ 6)°
A
x+ 4
D
M
2x – 3
F
13. Find the measure of each interior angle for a regular heptagon. Round to the nearest tenth if necessary.
Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false, find a
counterexample.
14. Acute angles measure less than 90 degrees.
Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.
15. Given: Point B is on ̅̅̅̅
𝐴𝐶
̅̅̅̅ ≅ 𝐵𝐶
̅̅̅̅
Conjecture: 𝐴𝐵
Find the coordinates of the midpoint of a segment having the given endpoints.
16.
17.
is an altitude,
, and
Z
A
X
W
Y
C
. Find
.
18. Triangle RSU is an equilateral triangle.
bisects
. Find x and y.
R
( y – 2)°
8x + 1
U
T
5x
S
19. Two angles are supplementary. One angle measures 32o more than the other. Find the measure of the two angles.
Determine whether a figure with the given vertices is a parallelogram. Use the method indicated.
20.
,
,
,
Distance and Slope Formulas
B
21. Where could you add point M on plane ACG so that A, C, and M would be collinear?
L
A
D
22. Name a point that is NOT coplanar with G, C, and L.
C
K
F
23. How many planes are shown in the figure?
G
Determine the relationship between the lengths of the given sides.
̅̅̅̅, 𝑌𝐷
̅̅̅̅
24. 𝑋𝑌
Z
48°
17°
X
42°
C
107°
46°
Y
98°
D
Identify the congruent triangles in the figure.
25. O
K
J
L
M
N
Determine the relationship between the measures of the given angles.
26. ∠𝑃𝑉𝑇, ∠𝑉𝑇𝑃
P
11
4
8 K
T
8
3
7
V 3 C
Determine whether statement (3) follows from statements (1) and (2) by the Law of Detachment or the Law of Syllogism. If
it does, state which law was used. If it does not, write invalid.
27. (1) You like the color green.
(2) Green is the color of brussel sprouts.
(3) You like brussel sprouts.
Determine whether
28.
and
are parallel, perpendicular, or neither.
Determine whether the quadrilateral is a parallelogram. Justify your answer.
70°
110°
29.
70°
110°
Use the Distance Formula to find the distance between each pair of points.
y
6
30.
5
4
T (2, 3)
3
2
1
–6
–5
–4
–3
–2
–1
–1
W (–4, –2)
1
2
3
4
5
6 x
–2
–3
–4
–5
–6
Find each measure.
31.
44°
47°
2
34°
1
3
32. Find the value of the variable and LN if M is between L and N.
Write the converse, inverse, and contrapositive of the conditional statement. Determine whether each statement is true or
false. If false, give a counterexample.
33. If two angles are complementary, then they form a right angle.
Find the distance between the pair of parallel lines.
34. 𝑦 = −2𝑥 − 1
𝑦 = −2𝑥 + 4
y
8
7
6
5
4
3
2
1
–8
–7
–6
–5
–4
–3
–2
–1
–1
–2
–3
–4
–5
–6
–7
–8
1
2
3
4
5
6
7
8 x
̅̅̅. Is this different from the
̅̅̅̅ and 𝐺𝐽
35. Using correct vocabulary explain the relationship between segments 𝐹𝐿
̅̅̅̅ and 𝐼𝐾
̅̅̅ ? Explain.
relationship between 𝐹𝐿
F
I
J
G
L
C
K
D
John has five straws. He wishes to use the straws to make a triangular design.
The straws measure 5 centimeters, 3 centimeters, 8 centimeters, 9 centimeters, and 14 centimeters.
36. How many different triangles could John make with the straws? List all possibilities.
Write a two-column proof to prove the following.
37. Given: ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐷𝐸 and ̅̅̅̅
𝐵𝐶 ≅ ̅̅̅̅
𝐸𝐹
̅̅̅̅
̅̅̅̅
Prove: 𝐴𝐶 ≅ 𝐷𝐹
Write a two-column proof.
38. Given: 𝛥𝐴𝐵𝐷 is equilateral
̅̅̅̅
𝐴𝐶 bisects ∠𝐴
Prove: C is the midpoint of ̅̅̅̅
𝐵𝐷.
A
B
D
C
Write an indirect proof.
̅̅̅̅̅ ≅ 𝑂𝑌
̅̅̅̅
̅̅̅̅̅ ≇ 𝑍𝑌
̅̅̅̅ and 𝑊𝑂
39. Given: 𝑊𝑋
Prove: ∠𝑊 ≇ ∠𝑌
X
W
O
Y
Z