Analytic Geometry
Unit 1 Section 6 RECOVERY Review
Name:____________________________________
1. If quadrilateral ABCD is a parallelogram, then which of the following statements must be true?
A.
B
C
B.
A
B
C.
A
C
D.
A
D
2. Which of the following is defined as a quadrilateral with sides of equal length?
A. rectangle
B. kite
C. rhombus
D. trapezoid
3. Which of the following are NOT sufficient to prove that a quadrilateral is a parallelogram?
I.
II.
III.
IV.
V.
VI.
VII.
Two pairs of opposite angles congruent.
Both pairs of opposite sides are parallel.
Both pairs of opposite sides are congruent.
The diagonals bisect each other.
A pair of adjacent angles are supplementary.
One pair of opposite sides are both parallel and congruent.
A pair of opposite sides parallel and the other pair of opposite sides congruent.
A. V and VII only
B. IV, V, and VI only
C. V, VI, and VII only
D. IV and VI only
4. Which of the following is defined as a quadrilateral with four right angles?
A. rhombus
B. rectangle
C. kite
D. trapezoid
5.
Given: Rhombus PQRS.
Prove: PR
QS
Proof:
Statements
1. PQ
QR
2. QS
QS
Reasons
RS
SRQ
4.
RQS
5. QC
Definition of a rhombus
Reflexive property of congruence
3. SPQ
PQS
SP
QC
Corresponding parts of congruent triangles are congruent.
Reflexive property of congruence
6. PQC
RQC
SAS
7.
RCQ
Corresponding parts of congruent triangles are congruent.
PCQ
8. PR
QS
If two intersecting lines form congruent adjacent angles, then they are
perpendicular.
Which of the following reasons completes the proof?
A. AAS
B. ASA
C. SSS
D. SAS
6. Which of the following is defined as a quadrilateral with sides of equal length and four right angles?
A. parallelogram
B. rectangle
C. rhombus
D. square
7. Which of the following quadrilaterals must have diagonals that bisect each other?
I. Rhombus
II. Isosceles Trapezoid
III. Rectangle
IV. Parallelogram
A. I, III, and IV
B. I and III
C. All of these.
D. III and IV
8. In rhombus ABCD, segments AC and BD are diagonals. If m DAB = 102°, what is the measure of
Note: Figure is not drawn to scale.
A. 129°
B. 141°
C. 219°
D. 39°
9. If quadrilateral ABCD is a parallelogram, then which of the following statements must be true?
A. m B + m C = 90°
B.
A
D
C. m A + m D = 180°
D. m A + m C = 180°
10. A trapezoid is always an example of a:
I. rectangle
II. rhombus
III. parallelogram
IV. square
A. I
B. II
C. IV
D. none of these
ABE?
11.
Given: Parallellogram PQRS with diagonals PR and QS intersecting at point T.
Prove: Point T is the midpoint of PR and QS.
Proof:
Statements
Reasons
1. PQ
Definition of parallelogram
2.
RS
QSR
PRS
SQP
RPQ
Alternate interior angles
3.
4. PQT
RST
ASA
5. QT ST
PT RT
Corresponding parts of congruent triangles are congruent.
6. T is the midpoint of PR.
Definition of a midpoint
T is the midpoint of QS.
Which of the following statements and reasons completes the proof?
A. PS QR; Opposite sides of a parallelogram are congruent
B. PQ
RS; Opposite sides of a parallelogram are congruent
C.
PTQ
RTS; Vertical Angles
D.
PTS
RTS; Vertical Angles
12. Which of the following statements would be sufficient to prove that parallelogram PQRS is a rectangle?
A.
P is the supplement of
B. m P = m
S
R
C. PS = QR
D. PR = QS
13. Which of the following is defined as a quadrilateral with both pairs of opposite sides parallel?
A. trapezoid
B. parallelogram
C. kite
D. isosceles trapezoid
14. A rhombus is always an example of a:
I. rectangle
II. parallelogram
III. square
IV. trapezoid
A. IV
B. I
C. II
D. none of these
15. Figure WXZY is a parallelogram. The measure of segment XZ is 6 inches and the measure of segment WX
is 21 inches. What is the measure of segment WY?
*Note: Figure not drawn to scale.
A. 12 inches
B. 27 inches
C. 21 inches
D. 6 inches
16. If the diagonals of a quadrilateral are perpendicular bisectors of equal length, then the quadrilateral must be
a
. (Give the strongest condition.)
A. square
B. rhombus
C. trapezoid
D. rectangle
17. What quadrilateral will have diagonals of equal length, but will have no right angles?
A. rectangle
B. square
C. rhombus
D. isosceles trapezoid
18. A rectangle is always an example of a:
I. rhombus
II. parallelogram
III. square
IV. trapezoid
A. II
B. IV
C. none of these
D. III
19.
Given: Parallelogram FGHJ with diagonal GJ.
Prove: FGJ
HJG
Proof:
Statements
Reasons
1. FG
Definition of parallelogram
2.
2
3. FJ
4.
HJ
6
Alternate interior angles are congruent.
Definition of parallelogram
GH
3
4
5. GJ
JG
6. FGJ
Alternate interior angles are congruent.
Reflexive property of congruence
HJG
Which of the following reasons completes the proof?
A. SSS
B. SAS
C. ASA
D. AAS
20. A parallelogram with four congruent sides and no right angles must be a
A. square
B. rhombus
C. trapezoid
D. rectangle
.
21. If quadrilateral ABCD is an isosceles trapezoid, then which of the following statements must be true?
A. m B + m C = 180°
B. m A + m D = 180°
C. m A + m B = 90°
D. m A + m B = 180°
22. A square is always an example of a:
I. rectangle
II. rhombus
III. parallelogram
IV. trapezoid
A. II
B. I, II, and III
C. none of these
D. I
23. A parallelogram is always an example of a:
I. rectangle
II. rhombus
III. square
IV. trapezoid
A. none of these
B. IV
C. I, II, III, and IV
D. I, II, and III
24. ABCD is a rhombus and ABC is an equilateral triangle. If the diagonal AC has a length of 8 cm, then what
is the length of segment AD?
A. 7 cm
B. 8
2) cm
C. 8 cm
D. 8
3) cm
25. Which of the following is defined as a quadrilateral with exactly one pair of opposite sides parallel?
A. trapezoid
B. square
C. rhombus
D. parallelogram
Answers
1. C
2. C
3. A
4. B
5. C
6. D
7. A
8. D
9. C
10. D
11. B
12. D
13. B
14. C
15. D
16. A
17. D
18. A
19. C
20. B
21. D
22. B
23. A
24. C
25. A