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Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Name Class Date
Practice Form G
Properties of Rhombuses, Rectangles, and Squares
Decide whether the parallelogram is a rhombus, a rectangle, or a square. Explain.
1. 2. 3.
4. 5.
Find the measures of the numbered angles in each rhombus.
6. 7.
8. 9.
10. 11.
12. 13.
Algebra HIJK is a rectangle. Find the value of x and the length of each diagonal.
14. HJ = x and IK = 2x - 7 15. HJ = 3x + 5 and IK = 5x - 9
16. HJ = 3x + 7 and IK = 6x - 11 17. HJ = 19 + 2x and IK = 3x + 22
54!
31
24
68!
31 2
4
20!
3
12
4
A B
CD
52!
31
2
4
3
12
459!29!
3
1 2
4
39!
3
1
2
449!
3
12
4
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Name Class Date
Practice (continued) Form G
Properties of Rhombuses, Rectangles, and Squares
Algebra HIJK is a rectangle. Find the value of x and the length of each diagonal.
18. HJ = 4x and IK = 7x - 12 19. HJ = x + 40 and IK = 5x
Determine the most precise name for each quadrilateral.
20. 21.
22. 23.
Algebra Find the values of the variables. Then find the side lengths.
24. square WXYZ 25. rhombus ABCD
26. rectangle QRST 27. square LMNO
28. Solve using a paragraph proof.
Given: Rectangle DVEO with diagonals DE and OV
Prove: △OVE ≅ △DEV
W
Z
X
Y
3x5
x ! 8
A
C
B
3m
m ! 12
D
3x ! 10
x R
ST
Q
4y
2y
M L x ! 7
O N
3x ! 1
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Name Class Date
Practice Form G
Conditions for Rhombuses, Rectangles, and Squares
Can you conclude that the parallelogram is a rhombus, a rectangle, or a square? Explain.
1. 2.
3. 4. NP ≅ OQ
For what value of x is the figure the given special parallelogram?
5. rhombus 6. rhombus 7. rectangle
8. rhombus 9. rectangle 10. rectangle
Open-Ended Given two segments with lengths x and y (x ≠ y), what special parallelograms meet the given conditions? Show each sketch.
11. One diagonal has length x, the other has length y. The diagonals intersect at right angles.
12. Both diagonals have length y and do not intersect at right angles.
C D
EF
O P
QR
R S
TU
N O
PQ
(6x ! 32)"
(17x # 1)"
(3x ! 12)"4x"
E F
GH
Q R
ST
5
2x ! 6
5
3x " 6
QS ≅ TR
M
m<PMN ! 110
N
OP
5x"
X Y
ZAAY ! XZ
6x " 3 5x
B O
MR MB ! RO
7x " 25x # 16
3
3
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Name Class Date
For Exercises 13–16, determine whether the parallelogram is a rhombus, a rectangle, or a square. Give the most precise description in each case.
13. A parallelogram has perpendicular diagonals and angle measures of 45, 135, 45, and 135.
14. A parallelogram has perpendicular and congruent diagonals.
15. A parallelogram has perpendicular diagonals and angle measures that are all 90.
16. A parallelogram has congruent diagonals.
17. A woman is plotting out a garden bed. She measures the diagonals of the bed and finds that one is 22 ft long and the other is 23 ft long. Could the garden bed be a rectangle? Explain.
18. A man is making a square frame. How can he check to make sure the frame is square, using only a tape measure?
19. A girl cuts out rectangular pieces of cardboard for a project. She checks to see that they are rectangular by determining if the diagonals are perpendicular. Will this tell her whether a piece is a rectangle? Explain.
20. Reasoning Explain why drawing both diagonals on any rectangle will always result in two pairs of nonoverlapping congruent triangles.
Practice (continued) Form G
Conditions for Rhombuses, Rectangles, and Squares
