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NAME ________________________
PER _______
DATE _______________________
ID: A
Pre-AP Geometry First Semester Review II
Find the measure of each angle.
8 Identify the intersection of plane SVX and plane
STU.
1 mÐ1 = _________
________
2 mÐ2 = _________
Use the figure below.
3 mÐ3 = _________
4 Write the inverse of the following statement.
If x = 2, then x + 3 = 5.
____________________
5 Determine whether 8, 4, and 2 can be the lengths of
the sides of a triangle. Write yes or no. Explain.
9 Name the intersection of the plane that contains
points A, B, and D and the plane P.
A point D
B triangle BCD
C AD
________________________
6 Find ST if S is between R and T, RS is 48 and RT is
57.
D
BD
10 Which three points in the figure are collinear?
F C, D, F
G A, E, F
H B, C, D
J A, D, E
___________
¬¾
¾
®
¬¾¾
®
¬¾¾
®
7 Determine whether CS and KP are parallel,
perpendicular, or neither.
C(-5, 6), S(-3, 2), K(-2, 10), P(1, 4)
____________________
1
16 Complete the proof.
Given: L is the midpoint of JM; JK € NM.
Prove: JKL @ MNL
11 In the diagram, AE € CD,mÐEAB = 59, and
mÐABC = 120. What is the measure of ÐBCD?
Statements
1. L is the midpoint of
JM.
2. JL @ ML
Use the figures below.
3. JK € MN
4. ÐJKL @ ÐMNL
5. ÐJLK @ ÐMLN
6.
12 If ÐABC @ ÐEFG, and mÐABC = 72, find
mÐGFH.
F 18
G 72
H 90
J 108
JKL @
MNL
Reasons
1. Given
2. Definition of
midpoint
3. Given
4. Alt. int. Ðs are @ .
5.
___________
6.
___________
17 Name the angle with greatest measure in
Identify each pair of angles as alternate interior,
alternate exterior, corresponding, or consecutive
interior angles.
A
B
C
D
DEF.
ÐD
ÐE
ÐF
cannot tell
18
ABC is an isosceles triangle with BD ^ AC. Then
name the postulate that could be used to prove
BDA @ BDC.
13 Ð2 and Ð12 _______________
14 Ð3 and Ð5 ________________
15 Given m € n and mÐ8 = 86, find mÐ13.
_________
________
2
19 List the sides of
longest.
PQR in order from shortest to
23 Complete this two-column proof.
Given: ABC is an isosceles triangle with base AC.
D is the midpoint of AC.
Prove: BD bisects ÐABC.
_____, _____, _____
Statements
1. ABC is isosceles with
base AC.
2. AB @ CB
3. ÐA @ ÐC
4. D is the midpoint of
AC.
5. AD @ CD
6. ABD @ CBD
7. Ð1 @ Ð2
8. BD bisects ÐABC.
20 Find the slope of a line perpendicular to the line
containing (-8, 10) and (0, 9).
__________
21 In rhombus YZ AB, if YZ =12, find AB.
Reason
1.
2.
3
4.
5.
6.
7.
8.
24 Determine wearther statement (3) is a valid
conclusion of statements (1) and (2)?
A
B
C
D
(1) If a quadrilateral has 4 right angles, then the
figure is a rectangle.
(2) A rectangle has 2 pairs of parallel sides.
(3) If a quadrilateral has 4 right angles, then the
figure has 2 pair of parallel sides.
24
12
6
12 2
22 Given: T is the midpoint of US .
What parts must be congruent to prove the triangles
congruent by SAS?
_________
25 Write the converse of the statement If two lines are
perpendicular to the same line, then they are
parallel.
________________________________
______________________________
________________
3
26 Find the coordinates of the point Q on WT that is
1
distance from W to T.
3
30 B is the midpoint of AC . Find the coordinates of A
if B(6,-3) and C (10,-5).
_________
31 What is the distance from the point B(-3,3) to the
line with equation y = 2x - 1.
__________
27 If a triangle has sides of a, a and x. Which of the
following statements must always be true?
A
B
C
D
x=a
x < 2a
x = 2a
x > 2a
__________
Refer to the figure to determine which is a true
statement for the given information.
32 To prove that the diagonals of a rhombus are
perpendicular to each other, you would position and
label a rhombus on a coordinate plane and then find
which of the following?
F
G
H
J
28 FG is an altitude.
F ÐDGF is a right angle.
G DF = EF
H DG = GE
J ÐDFG @ ÐEFG
29 FG is a median.
A ÐDGF is a right angle.
B DF = EF
C DG = GE
D ÐDFG @ ÐEFG
4
measures of the angles
slopes of the diagonals
lengths of the diagonals
midpoints of the diagonals
On a notebook piece of paper write a flow proof.
33 If the measure of each interior angle of a regular
polygon is 176. Find the number of sides on the
polygon.
38 Given: R is the midpoint of SU ; SV @ UV .
Prove: DRSV @ DRUV
_______________
34 A convex hexagon has interior angles with measures
x°, (5x - 103)°, (2x + 60)°, (7x - 31)°, (6x - 6)°,
and (9x - 100)°. Find x.
39 Given: W is the midpoint of XY and VZ .
Prove: DXVW @ DYZW
_________________
35 What is the slope of a line parallel to the line
containing (2, 5) and (6, -11)?
__________
40 Given: M is the midpoint of LN ; ÐLMP @ ÐNMO;
ON ^NM ; PL^LM
Prove: DNMO @ DLMP
36 Find the slope of a line perpendicular to the line
containing (-2, -9) and (8, 6).
__________
37 Suppose line a is perpendicular to line b and line b
is parallel to line c. What is the relationship between
line a and line c?
___________
5
ID: A
Pre-AP Geometry First Semester Review II
Answer Section
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140
50
If x ¹ 2, then x + 3 ¹ 5.
no; 2 + 4 < 8
9
parallel
¬¾
¾
®
SV
D
J
x
F
alternate exterior
alternate interior
94
Vertical angles are congruent
AAS
A
HL or AAS
PQ, PR, QR
8
B
<UTR = <STR
SAS
CPCTC
Def, of Angle Bisector
Valid
If two lines are €, then they are ^ to the same line.
æç 1
ö
çç -1 ,-4 ÷÷÷
çç 3
÷÷
è
ø
B
F
C
(2,-1)
20 = 2 5 » 4.47
G
90
30
-4
1
ID: A
2
3
37 a ^ c
38 Sample:
Given: R is the midpoint of SU ; SV @ UV .
Prove: DRSV @ DRUV
Proof:
Statements
Reasons
1. Given
1. R is the midpoint of SU .
2. Midpoint Theorem
2. RS @ RU
3. Given
3. SV @ UV
4. Reflexive Property
4. RV @ RV
5. DRSV @ DRUV
5. SSS Postulate
39 Sample:
Given: W is the midpoint of XY and VZ .
Prove: DXVW @ DYZW
Proof:
Statements
Reasons
1. Given
1. W is the midpoint of XY .
2. Midpoint Theorem
2. XW @ YW
3. Given
3. W is the midpoint of VZ .
4. Midpoint Theorem
4. ZW @ VW
5. ÐXWV and ÐYWZ are vertical angles.
5. Definition of vertical angles
6. ÐXWV @ ÐYWZ
6. Vertical angles are congruent.
7. DXVW @ DYZW
7. SAS Postulate
40 ample:
Given: M is the midpoint of LN ; ÐLMP @ ÐNMO.
Prove: DNMO @ DLMP
Proof:
36 -
2