Rhombi, Rectangles and...

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April 24, 2017

Rhombi, Rectanglesand Squares

Return to the Table of ContentsMath Practice

The Response Q's in this lesson address MP1, MP2 & MP7.

Additional Q's to address MP standards:What information are you given? (MP1)What do you need to find? (MP1)How can you represent the problem with numbers and symbols? (MP2)How are the properties of rhombi, rectangles & squares related to algebraic equations? (MP7)


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Three Special Parallelograms

Rhombus Rectangle

Square

All the same properties of a parallelogram apply to the rhombus, rectangle, and square.


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A rhombus is a quadrilateral with four congruent sides.

A B

CD

If AB ≅ BC ≅ CD ≅ DA,then ABCD is a rhombus.

Rhombus


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66 What is the value of y that will make the quadrilateral a rhombus?

A 7.25

B 12

C 20

D 25

35y

12

Answer

C


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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

Answer

A


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A B

CD

O

The diagonals of a rhombus are perpendicular.

Since ABCD is a parallelogram, its diagonals bisect each other.

AO ≅ CO and BO ≅ DO.

Theorem


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If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.

If ABCD is a rhombus, then

∠DAC ≅ ∠BAC ≅∠BCA ≅ ∠DCA

and

∠ADB ≅ ∠CDB ≅ ∠ABD ≅ ∠CBD

Theorem

A B

CD


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68 EFGH is a rhombus. Find the value of x.

E F

G H

72°z°

2x 6

5y

10

Answer


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E F

G H

72°z°

2x 6

5y

10

69 EFGH is a rhombus. Find the value of y.

Answer


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E F

G H

72°z°

2x 6

5y

10

70 EFGH is a rhombus. Find the value of z.

F

Answer


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71 This quadrilateral is a rhombus. Find the value of x.

8

86°

3x + 2

z°

12y2

Answer


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72 This quadrilateral is a rhombus. Find the value of y.

8

86°

3x + 2

z°

12y2

Answer


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73 This quadrilateral is a rhombus. Find the value of z.

8

86°

3x + 2

z°

12y2

Answer


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74 This is a rhombus. Find the value of x.

x°

Answer

90


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13x 3

9

Answer

36


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126°x°

Answer


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77 HJKL is a rhombus. Find the length of HJ.

H J

KL

6 M16

Answer


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A B

CD

A rectangle is a quadrilateral with only right angles.

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.

Rectangles


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78 What value of y will make the quadrilateral a rectangle?

(6y)°

12 Answer

15


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The diagonals of a rectangle are congruent.

If ABCD is a rectangle, then AC ≅ BD.

Also, since a rectangle is a parallelogram,

AM ≅ BM ≅ CM ≅ DM

A B

CD

M

Theorem


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79 RECT is a rectangle. Find the value of x.

2x 5 13

63°(9y)°

R E

CT

Answer Option A

2x 5 = 132x = 18x = 9


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80 RECT is a rectangle. Find the value of y.

2x 5 13

63°(9y)°

R E

CT

Answer

The measure of each angle in a rectangle is 90°.


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81 RSTU is a rectangle. Find the value of z.

R S

TU(8z)°

Answer

11.25


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82 RSTU is a rectangle. Find the value of z.

R S

TU

4z 9

7

Answer


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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.

Square


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83 This quadrilateral is a square. Find the value of x.

z 4

(5x)°

6

(3y)° Answer

In a rhombus the diagonals are perpendicular.


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84 This quadrilateral is a square. Find the value of y.

z 4

(5x)°

6

(3y)° Answer

In a rhombus the diagonals are perpendicular.


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z 4

(5x)°

6

(3y)°

85 This quadrilateral is a square. Find the value of z.

Answer


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86 This quadrilateral is a square. Find the value of x.

y 2

(12z)°

10 3y

(x2 + 9)°

Answer


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y 2

(12z)°

10 3y

(x2 + 9)° Answer


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88 This quadrilateral is a square. Find the value of z.

y 2

(12z)°

10 3y

(x2 + 9)°

Answer


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(18y)°

Answer


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90 This quadrilateral is a rhombus. Find the value of x.

2x + 6

4x

Answer


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112°

(4x)°

91 The quadrilateral is parallelogram. Find the value of x.

Answer


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92 The quadrilateral is a rectangle. Find the value of x.

10x

3x + 7

Answer

1


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Opposite sidesare ||

Diagonals bisectopposite ∠'s

Has 4 ≅ sides

Has 4 right ∠'sDiagonals are

Fill in the Table with the Correct Definition

rhombus rectangle square

Answer

Opposite sidesare ||

Diagonals are ≅


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Lab Quadrilaterals in the Coordinate Plane

Math Practice


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Trapezoids

Return to theTable of Contents


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A trapezoid is a quadrilateral with one pair of parallel sides.

base

legbase angles

base

leg

The parallel sides are called bases.

The nonparallel sides are called legs.

A trapezoid also has two pairs of base angles.

Trapezoid


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An isosceles trapezoid is a trapezoid with congruent legs.

Isosceles Trapezoid

Rhombi, Rectangles and...

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