Name____________________________________
Review for Test: Aims 28 – 34
Date__________
1. Which statement is not always true about a parallelogram?
1) The diagonals are congruent.
2) The opposite sides are congruent.
3) The opposite angles are congruent.
4) The opposite sides are parallel.
2. Given three distinct quadrilaterals, a square, a rectangle, and a rhombus, which
quadrilaterals must have perpendicular diagonals?
1) the rhombus, only
2) the rectangle and the square
3) the rhombus and the square
4) the rectangle, the rhombus, and the square
3. Which statement is false?
1) All parallelograms are quadrilaterals.
2) All rectangles are parallelograms.
3) All squares are rhombuses.
4) All rectangles are squares.
4. In the diagram below, parallelogram ABCD has diagonals AC and BD that intersect at
point E.
Which expression is not always true?
1)
DAE 
BCE
2)
DEC 
BEA
3) AC  DB
4) DE  EB
5. In parallelogram QRST, diagonal QS is drawn. Which statement must always be true?
1) QRS is an isosceles triangle.
2) STQ is an acute triangle.
3) STQ  QRS
4) QS  QT
6. Which quadrilateral does not always have congruent diagonals?
1) isosceles trapezoid
2) rectangle
3) rhombus
4) square
7. In quadrilateral ABCD, the diagonals bisect its angles. If the diagonals are not
congruent, quadrilateral ABCD must be a
1) square
2) rectangle
3) rhombus
4) trapezoid
8. Which reason could be used to prove that a parallelogram is a rhombus?
1) Diagonals are congruent.
2) Opposite sides are parallel.
3) Diagonals are perpendicular.
4) Opposite angles are congruent.
9. A parallelogram must be a rectangle when its
1) diagonals are perpendicular
2) diagonals are congruent
3) opposite sides are parallel
4) opposite sides are congruent
10.
1)
2)
3)
4)
A parallelogram must be a rhombus when its
Opposite sides are congruent.
Opposite sides are parallel.
Diagonals bisect each other.
Adjacent sides are congruent.
11. Quadrilateral ABCD has diagonals AC and BD .
Which information is not sufficient to prove ABCD is a parallelogram?
1) AC and BD bisect each other.
2) AB  CD and BC  AD
3) AB  CD and AB CD
4) AB  CD and BC AD
12. In rhombus ABCD, with diagonals AC and DB , AD = 10. If the length of diagonal AC
is 12, what is the length of DB ?
13. In parallelogram ABCD, diagonals AC and BD intersect at E.
If AE = x + 7, EC = 2x – 1 and BD = 4x – 2, determine if ABCD is a rectangle.
Justify your answer.
14. In parallelogram ABCD, diagonals AC and BD intersect at E. If ∡BAE = 5x – 5,
∡ABE = 3x + 23 and ∡ BDC = 2x + 32:
a) Is ABCD a rhombus? Justify your answer.
b) Is ABCD a square? Justify your answer.
15. In the diagram below of ABC , DE is a midsegment of ∆ABC, AD = 4, AC = 10 and
BC = 12. Find the perimeter of BDE .
16. In the diagram of ABC shown below, D is the midpoint of AB , E is the midpoint
of BC , and F is the midpoint of AC .
If AB
1)
2)
3)
4)
= 20, BC = 12, and AC = 16, what is the perimeter of quadrilateral ABEF?
24
36
40
44
17. In ABC , D is the midpoint of AB and E is the midpoint of BC . If AC = 3x - 15 and
DE = 6, what is the value of x?
18. A triangle has sides of lengths 12, 16 and 20.
What is the perimeter of the triangle formed by connecting the midpoints of the sides
of the triangle?
a) 24
b) 48
c) 96
d) 50
19. In the triangle below, D is the midpoint of AC and E is the midpoint of BC .
If DE = 3x – 7 and AB = 4x + 6, find the length of AB .
A
D
C
E
B
20. Given: ABCD is a parallelogram,
AF CE
Prove: ABF  CDE
Statements
Reasons
A
21.
B
Given: AD CB , AE  CF , AE  DB , CF  DB
F
Prove: ABCD is a parallelogram.
E
D
Statements
Reasons
22. Given: parallelogram ABCD, BE  CD , DF  BC , CE  CF .
Prove: ABCD is a rhombus.
Statements
Reasons
C
23. Given: Parallelogram DEFG,
DGK 
EFH
Prove: DK  EH
Statements
24.
Reasons
Given: Rectangle ABCD with points E and F on side AB .
CE and DF intersect at G, and
ADG 
BCG .
Prove: AE  BF
Statements
Reasons
25. Given: Parallelogram ABCD, diagonals AC and BD intersect at E
a) Prove: AED  CEB
Statements
Reasons
b) Describe a single rigid motion that maps AED onto CEB .
26. Using your compass and ruler, construct  ABC congruent to  DEF using the SAS
congruence criteria.
D
E
F