Quadrilateral Review

Quadrilateral Review

Everything I need you to know is right here in this quizz. Update your notes as you go along if you need to. The test is open note so I would recommend writing down these examples to look back at later.

Good luck! Make Grogu proud.

Properties of Parallelograms

Definition: A Quadrilateral where both pairs of opposite sides are parallel. 

1) Opposite sides are congruent.
2) Opposite angles are congruent.
3) Consecutive angles are supplementary.
4) Diagonals bisect each other.

Multiple Choice

Find the measurement indicated in each parallelogram.

• A

• B

• C

• D

Multiple Choice

If GI = 2s - 84 and GK = s-18. Find the value of S

• 12
• 55
• 66
• 60

Multiple Choice

The figure is a parallelogram.  
Solve for x.  

• 7
• 2
• 0
• 4

Multiple Choice

The figure is a parallelogram.

Solve for x.

• 1

• 11

• 7

• 6

Properties of Rectangles

Definition: A parallelogram with 4 right angles and the opposite sides are congruent.

1) The diagonals of a rectangle bisect each other.

Rectangles also have ALL of the same properties as a parallelogram.

Multiple Choice

Find x.

• x = 7

• x = 11

• x = 5

• x = 13

Multiple Choice

If the figure is a rectangle, the value of x is...

• 2
• 12
• 13
• 28

Properties of a Rhombus

Definition: A parallelogram with 4 congruent sides.

1) Each diagonal bisects a pair of opposite angles.

2) The diagonals of a rhombus are perpendicular.

Rhombi also have ALL of the same properties as a parallelogram.

Multiple Choice

Find y.

• 2
• 4
• 6
• 8

Multiple Choice

Given Rhombus TUVW. Find m∠2.

• 62

• 28

• 90

• 78

Multiple Choice

TUVW is a rhombus.  Find m∠3.

• 62
• 28
• 90
• 78

Multiple Choice

Given Rhombus TUVW. Find m∠4.

• 62
• 28
• 90
• 78

Properties of Squares

Definition: A parallelogram with 4 right angles and 4 congruent sides.

Squares have no unique properties BUT...

They have ALL the properties of Parallelograms, Rhombus and Rectangles.

Multiple Choice

All rectangles are squares.

• True
• False

Multiple Choice

All squares are rhombuses.

• True
• False

Multiple Choice

All squares are parallelograms.

• True
• False

Multiple Choice

In a square, the diagonals are...

• bisect the angles
• perpendicular
• congruent
• all of the above

Multiple Choice

MNKL is a square. Find the measure of angle MKN.

• 180 degrees

• 90 degrees

• 60 degrees

• 45 degrees

Properties of Trapezoids

Definition: A Quadrilateral with exactly ONE pair of parallel sides.

1) Angles formed by legs are supplementary.

Multiple Choice

What is the height of this trapezoid?

• 8.5 m

• 6.5 m

• 3.5 m

• 3 m

Multiple Choice

Find the value of x.

• 7
• 8
• 85
• None of these

Properties of Kites

Definition: A quadrilateral with 2 pairs of congruent sides BUT opposite sides are NOT congruent.

1) Diagonals are perpendicular.

2) One diagonal is bisected by the other but not both.

3) One diagonal bisects its angles but both don't.

Multiple Choice

Find the value of x that makes that shape a kite.

• x = 4.5

• x= 4

• x = 2

• x = 5

Multiple Choice

What is x?

• 35
• 45
• 55
• 90

Multiple Choice

Find the value of y.

• 65

• 110

• 75

• None of these.

Multiple Choice

Which of the following statements is true?

• the diagonals bisect each other
• the diagonals are congruent
• ∠B and ∠D  are congruent
• DB bisects AC

Multiple Choice

Which of the following statements is false?

• BD and AC are perpendicular
• BD and AC are congruent
• ∠A and ∠C  are congruent
• BD bisects AC

Properties of an Isosceles Trapezoid

Definition: A trapezoid with congruent legs.

1) The diagonals are congruent.

2) Angles formed by legs are supplementary

3) The angles formed by base 1 are congruent to each other.

4) The angles formed by base 2 are congruent to each other.

Multiple Choice

What is the measure of ∠P?

• 65 degrees
• 115 degrees
• 180 degrees
• None of the above

Multiple Choice

What is the measure of ∠A?

• 15 degrees
• 115 degrees
• 180 degrees
• None of the above

Multiple Choice

Find the measure of n:

• 117
• 63
• 25
• 39

Multiple Choice

XV = 4.6, and WY = 14.2. Find VZ.

• 9.6
• 9.2
• 8 
• 14.2

Area of Trapezoids

 $A=\frac{\left(b_1+b_2\right)}{2}\cdot h$  

Multiple Choice

Find the area of a trapezoid with bases of 5 feet and 7 feet, and a height of 3 feet.

• 18 
• 36
• 72
• 40

Multiple Choice

Find the area of the trapezoid.

• 18 m²
• 165 m²
• 84 m²
• 22.5 m²

Multiple Choice

Find the Area.

• 91 ft²

• 77 ft²

• 78 ft²

• 105 ft²

Area of Parallelograms

 $A=b\cdot h$  

Multiple Choice

A parallelogram has a base of 5in and a height of 4 in. What is the area of the parallelogram?

• 20 in²

• 9 in²

• 5 in²

• 1 in²

Multiple Choice

What is the area of the parallelogram above?

• 13 cm²

• 28.5 cm²

• 45.6 cm²

• 40 cm²

Area of Rectangles and Squares

 $A=l\cdot w\$ OR  $A=b\cdot h$  

Multiple Choice

What is area of this square?

• 90m

• 90m²

• 900m²

• 900m

Multiple Choice

What is the area of this rectangle?

• 8cm

• 15cm

• 15cm²

• 16cm

Area of a Kite and Rhombus

 $A=\frac{\left(d_1\cdot d_2\right)}{2}$  

Multiple Choice

Find the area. Remember to find the diagonals first. 

• 19.5 m2

• 78 m²

• 39 m²

• 27 m²

Multiple Choice

What is the area of this rhombus?
d1 = 12     d2= 4           

• 48 cm²

• 24 cm²

• 16 cm²

• 32cm²

Volume of a Sphere

 $V=\frac{4}{3}\pi r^3$  

Multiple Choice

What is the volume, in cubic meters, of the sphere?

• 602.88

• 1808.64

• 57876.48

• 7238.23

Volume of a Cylinder

 $V=B\cdot h$  OR  $V=\pi r^2\cdot h$  

Multiple Choice

Find the volume of the Cylinder. Round to the nearest whole number.

• 7230

• 6621

• 1131

• 907

Volume of Cone

 $V=\frac{\left(B\cdot h\right)}{3}$  OR  $V=\frac{\left(\pi r^2\cdot h\right)}{3}$  

Multiple Choice

What is the volume, in cubic inches, of the cone?

• 33.49

• 134.04

• 401.92

• 267.95

Volume of a Rectangular Prism

 $V=B\cdot h$  OR  $V=l\cdot w\cdot h$  

Multiple Choice

What is the volume of this prism?

• 24 cubic cm

• 240 cubic cm

• 60 cubic cm

Volume of Square Pyramid

 $V=\frac{\left(B\cdot h\right)}{3}$  OR  $V=\frac{\left(l\cdot w\cdot h\right)}{3}$  

Multiple Choice

Find the volume of the figure.

• 126 cm³

• 907.5 cm³

• 605 cm³

• 55 cm³