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NAME ________________________
PER _______
DATE _______________________
ID: A
Pre-AP Geometry First Semester Review I
Use the figure below.
5 Find the coordinates of a point Q if P is the midpoint
of NQ.
1 Name the intersection of planes A and B.
_________
_____
2
6 What is the distance from R to q shown in the
figure?
How many non-collinear points are needed to
determine a plane?
_____
3 Five points A, B, C, D, and E are collinear, not
necessarily in that order. AB has a length of 24.
Point C is the midpoint of AB, and ponit D is the
midpoint of AC . If the distance between D and E is
5, what is one possible distance between A ane E?
__________
_________
4 Find two possible lengths for CD if C, D, and E are
collinear, CE = 15.8 centimeters, and DE = 3.5
centimeters.
7
¾¾
¾
®
¾¾
®
In the figure above, PC bisects ÐBPD and PB
bisects ÐDPA. If ÐDPA is 146 0 , what is the
measure of ÐCPD?
CD = __________ and __________
_________
1
Use the figure below.
Use the figures below.
11 If mÐABC = 34, find mÐCBD.
A 90
B 56
C 45
D 34
8 Find mÐVSW if ÐWSR and ÐVSW are
complementary and mÐWSR is four times mÐVSW.
12 If ÐABC @ ÐEFG and mÐABC = 41, find
mÐGFH.
F 59
G 49
H 41
J 39
___________
9 Which pair of angles are supplementary?
A ÐUSV, ÐVSW
B ÐVSW, ÐWSR
C ÐTSV, ÐVSW
D ÐTSR, ÐUSW
13 Determine wearther statement (3) is a valid
conclusion of statements (1) and (2)?
(1) If all the sides of a quadrilateral are equal, then it
is a rhombus.
(2) ABCD is a quadrilateral with all sides equal.
(3) ABCD is a rhombus.
10 Which angle is a vertical angle to ÐUST?
F ÐVSW
G ÐUSV
H ÐTSR
J ÐWSR
___________
All paralellograms are quadrilaterals.
14 a. Write the statement in if-then form.
b. Write the converse, inverse, and contrapositive.
c. Give the truth value of each statement.
_______________________________________________________________, _____
______________________________________________________________, _____
______________________________________________________________, _____
______________________________________________________________, _____
2
18 Use the graph on #17. Find the coordinates of the
1
point Q on AB that is distance from A to B.
4
15 In the diagram, AE € CD,mÐEAB = 62, and
mÐBCD = 55. What is the measure of ÐABC ?
____________
Refer to the figure below. Identify the special
name for each angle.
mÐABC = _____
¬¾
¾
®
¬¾¾
®
Determine whether CS and KP are parallel,
perpendicular, or neither.
16 C(1, -12), S(5, 4), K(1, 9), P(6, -6)
19 Given p € q and mÐ3 = 75, find mÐ5.
A 15
B 75
C 105
D 120
_____________
17 Which of the following equations best represents the
perpendicular bisector of AB?
20 Given Ð1 @ Ð5, which postulate or theorem justifies
that p € q?
F If corresponding angles are congruent, then lines
are parallel.
G If consecutive interior angles are supplementary,
then lines are parallel.
H If alternate exterior angles are congruent, then
lines are parallel.
J If alternate interior angles are congruent, then
lines are parallel.
21 If Ð12 @ Ð14, which postulate or theorem justifies
that p € q?
A If corresponding angles congruent, then lines are
parallel.
B If consecutive interior angles are supplementary,
then lines are parallel.
C If alternate exterior angles are congruent, then
lines are parallel.
D If alternate interior angles are conguent, then
lines are parallel.
__________
3
26 If MLT @ MNT, what is used to prove Ð1 @
Ð2?
F CPCTC
G definition of isosceles triangle
H definition of perpendicular
J definition of angle bisector
22 If p € q because consecutive interior angles are
supplementary, then which angle pair must be
supplementary?
F Ð3 and Ð10
G Ð3 and Ð8
H Ð8 and Ð13
J Ð15 and Ð16
27 What are the congruent triangles in the diagram?
Use the figure below.
A
B
C
D
23 What is mÐ2?
ABC @
ABE @
AEB @
ABE @
EBD
CBD
CBD
CDB
__________
24 What is mÐ4?
28
__________
Use the figure.
KLM is an isosceles triangle and Ð1 @ Ð2. Name
the postulate that could be used to prove LKP @
LMN.
________
29 Given A is between Y and Z and YA = 14x, AZ = 10x
and YZ = 12x + 48. Find AZ.
_____________
25 If LMN is isosceles and T is the midpoint of LN,
which postulate can be used to prove MLT @
MNT?
A AAA
B AAS
C SAS
D ABC
.
4
Refer to the figure to determine which is a true
statement for the given information.
30 Complete the proof.
Given: DA € YN; DA @ YN
Prove: ÐNDY @ ÐDNA
Statements
1. DA € YN
2. ÐADN @ ÐYND
3. DA @ YN
4. DN @ DN
5. NDY @ DNA
6. ÐNDY @ ÐDNA
2. Alt. int. Ðs are @ .
3. Given
4. Reflexive Property
5. _____________
6. _____________
31 Name the longest side of
A
B
C
D
33 YW is an altitude.
A ÐYWZ is a right angle.
B ÐXYW @ ÐZYW
C XW = WZ
D XY = ZY
Reasons
1. Given
34 YW
F
G
H
J
DEF.
35 Which of the following sets of numbers can be the
lengths of the sides of a triangle?
A 6, 6, 12
B 6, 7, 13
2 , 5 , 15
C
D 2.6, 8.1, 10.2
DE
EF
DF
cannot tell
36 What is the relationship between the measures of Ð1
and Ð2?
32 Find the possible values for mÐ1.
F
G
H
J
is a median.
ÐYWZ is a right angle.
ÐXYW @ ÐZYW
XW = WZ
XY = ZY
F
G
H
J
mÐ1 > 62
mÐ1= 62
mÐ1 < 62
mÐ1 = 118
mÐ1 = mÐ2
mÐ1 < mÐ2
mÐ1 > mÐ2
cannot tell
37 List the angles of
greatest measure.
GHI in order from least to
_____, _____, _____
5
38 Write an inequality to compare EF and GH.
44 For isosceles trapezoid MNOP, find mÐMNQ.
________
________
45 For parallelogram ABCD, find mÐ1.
39 A convex pentagon has interior angles with
measures (5x - 12)°, (2x + 100)°, (4x + 16)°, (6x +
15)°, and (3x + 41)°. Find x.
______
_______
46 For rhombus ABCD, If mÐ1= 6x 2 - 6, find x.
40 The measures of two sides of a triangle are 14 feet
and 29 feet. If the measure of the third side is x
meters, find the range for x.
__________
_________________
47 To prove that the diagonals of a square bisect each
other, you would position and label a square in the
coordinate plane and then find which of the
following?
A measures of the angles
B midpoints of the diagonals
C lengths of the diagonals
D slopes of the diagonals
41 Find the sum of the measures of the exterior angles
of a convex 21-gon.
__________
42 Find the measure of each exterior angle of a regular
45-gon.
_____
48 On your own notebbok paper write a two-column
proof.
43 If the measure of each interior angle of a regular
polygon is 108, find the measure of each exterior
angle.
__________
Given: AB || DE, AD bisects BE.
Prove: DABC @ DDEC by using the ASA postulate.
6
49 On your own notebook paper write a flow proof.
Given: W is the midpoint of VZ ; ÐWVX @ ÐWZY .
Prove: DXVW @ DYZW
50 On your own paper write a two-column proof.
Given: Square GHJK
Prove: DGHK @ DJKH
7
ID: A
Pre-AP Geometry First Semester Review I
Answer Section
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36
¬¾
¾
®
RS
3
1 or 11
12.3 cm and 19.3 cm
çæ 1, - 1 ÷ö
è
ø
4.24
36.5
18
C
J
B
G
Valid
If , then True
Converse: If , then. False
Inverse: If , then . False
Contrapositive: If s, then. True
117
neither
y=x+2
(-2.5, 2.5)
B
F
C
G
50
100
C
F
B
AAS
x = 4, AZ = 40
SAS
CPCTC
C
F
A
H
D
H
1
ID: A
37
38
39
40
41
42
43
44
45
46
47
48
ÐI, ÐH, ÐG
EF < GH
19
15 ft < x < 43 ft
360
8
72
16
65
x = 4 or -4
B
Statements
1.AB || DE
2. ÐABC @ ÐDEC
3. AD bisects BE.
4. BC @ BC
5. ÐACB @ ÐDCE
6. DABC @ DDEC
49 Sample:
Given: W is the midpoint of XY
Prove: DXVW @ DYZW
Proof:
50 Sample:
Given: Square GHJK
Prove: DGHK @ DJKH
Proof:
Statements
1. GHJK is a square.
2. GK @ JH
3. GH @ JK
4. HK @ KH
5. DGHK @ DJKH
Reasons
1.Given
2. Alt. int. Ðs are @.
3. Given
4. Definition of segment bisector
5. Vert. Ðs are @
6. ASA
and VZ ; ÐWVX @ ÐWZY .
Reasons
1. Given
2. Definition of a square
3. Definition of a square
4. Reflexive Property
5. SSS Postulate
2