Rhombi, Rectangles and Squares


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1 Rhombi, Rectangles and Squares Math Practice Return to the Table of Contents 1
2 Three Special Parallelograms All the same properties of a parallelogram apply to the rhombus, rectangle, and square. Rhombus Rectangle Square 2
3 Rhombus A rhombus is a quadrilateral with four congruent sides. A B If AB BC CD DA, then ABCD is a rhombus. D C 3
4 66 What is the value of y that will make the quadrilateral a rhombus? A 7.25 B 12 C 20 D y 4
5 67 What is the value of y that will make this parallelogram a rhombus? A 7.25 B 12 C 20 D 25 2y+29 6y 5
6 Theorem The diagonals of a rhombus are perpendicular. A B O Since ABCD is a parallelogram, its diagonals bisect each other. AO CO and BO DO. D C 6
7 Theorem If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles. A B If ABCD is a rhombus, then D C DAC BAC BCA DCA and ADB CDB ABD CBD 7
8 68 EFGH is a rhombus. Find the value of x. 5y E 72 2x 6 z F G 10 H 8
9 69 EFGH is a rhombus. Find the value of y. 5y E 72 2x 6 z F G 10 H 9
10 70 EFGH is a rhombus. Find the value of z. E 2x 6 F 5y 72 z G 10 H 10
11 71 This quadrilateral is a rhombus. Find the value of x. 8 z 86 3x + 2 1y
12 72 This quadrilateral is a rhombus. Find the value of y. 8 z 86 3x + 2 1y
13 73 This quadrilateral is a rhombus. Find the value of z. 8 z 86 3x + 2 1y
14 74 This is a rhombus. Find the value of x. x 14
15 75 This is a rhombus. Find the value of x. 1 3 x
16 76 This is a rhombus. Find the value of x. 126 x 16
17 77 HJKL is a rhombus. Find the length of HJ. H J 6 M 16 L K 17
18 Rectangles A rectangle is a quadrilateral with only right angles. A B D C If ABCD is a rectangle, then A, B, C and D are right angles. If A, B, C and D are right angles, then ABCD is a rectangle. 18
19 78 What value of y will make the quadrilateral a rectangle? (6y) 12 19
20 Theorem The diagonals of a rectangle are congruent. A B M D C If ABCD is a rectangle, then AC BD. Also, since a rectangle is a parallelogram, AM BM CM DM 20
21 79 RECT is a rectangle. Find the value of x. R 63 (9y) E 2x 5 13 T C 21
22 80 RECT is a rectangle. Find the value of y. R 63 (9y) E 2x 5 13 T C 22
23 81 RSTU is a rectangle. Find the value of z. R S U (8z) T 23
24 82 RSTU is a rectangle. Find the value of z. R S 4z 9 7 U T 24
25 Square A square is a quadrilateral with equal sides and equal angles. It is, therefore both a rhombus and a rectangle. A square has all the properties of a rectangle and rhombus. 25
26 83 This quadrilateral is a square. Find the value of x. 6 z 4 (5x) (3y) 26
27 84 This quadrilateral is a square. Find the value of y. 6 z 4 (5x) (3y) 27
28 85 This quadrilateral is a square. Find the value of z. z 4 6 (5x) (3y) 28
29 86 This quadrilateral is a square. Find the value of x. y 2 (12z) 10 3y (x 2 + 9) 29
30 87 This quadrilateral is a square. Find the value of y. y y (12z) (x 2 + 9) 30
31 88 This quadrilateral is a square. Find the value of z. y 2 (12z) 10 3y (x 2 + 9) 31
32 89 This quadrilateral is a square. Find the value of y. (18y) 32
33 90 This quadrilateral is a rhombus. Find the value of x. 4x 2x
34 91 The quadrilateral is parallelogram. Find the value of x. 112 (4x) 34
35 92 The quadrilateral is a rectangle. Find the value of x. 10x 3x
36 Fill in the Table with the Correct Definition rhombus rectangle square Opposite sides are Diagonals are Diagonals bisect opposite 's Has 4 right 's Has 4 sides Diagonals are 36
37 Lab Quadrilaterals in the Coordinate Plane Math Practice 37
38 Trapezoids Return to the Table of Contents 38
39 Trapezoid A trapezoid is a quadrilateral with one pair of parallel sides. base leg base angles leg base The parallel sides are called bases. The nonparallel sides are called legs. A trapezoid also has two pairs of base angles. 39
40 Isosceles Trapezoid An isosceles trapezoid is a trapezoid with congruent legs. 40
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