Quadrilaterals: Properties, Types, and Theorems for 7th Grade Math

Question 1

Which of the following is NOT a characteristic of a rectangle?

Accepted Answer

Opposite sides are perpendicular

Answer

Opposite sides are parallel and congruent

Answer

Diagonals are congruent

Answer

Angles measure 90 degrees

Question 2

Which theorem states that the diagonals of a parallelogram bisect each other?

Accepted Answer

Parallelogram Diagonals Bisector Theorem

Answer

Triangle Midsegment Theorem

Answer

Pythagorean Theorem

Answer

Triangle Sum Theorem

Question 3

A quadrilateral that is both a rectangle and a parallelogram is a:

Accepted Answer

Rhombus and a rectangle

Answer

Rectangle and a parallelogram

Answer

Trapezoid and a rhombus

Answer

Parallelogram and a rhombus

Question 4

A quadrilateral with two pairs of adjacent congruent sides is called a:

Accepted Answer

Kite

Answer

Square

Answer

Rectangle

Answer

Parallelogram

Question 5

Which theorem states that opposite angles of a parallelogram are congruent?

Accepted Answer

Parallelogram Opposite Angles Theorem

Answer

Triangle Sum Theorem

Answer

Triangle Angle Bisector Theorem

Answer

Pythagorean Theorem

Question 6

A necessary condition for a quadrilateral to be a square is that:

Accepted Answer

All sides are congruent

Answer

Opposite sides are parallel

Answer

Diagonals bisect each other

Answer

All angles are congruent

Question 7

Which quadrilateral has four equal sides and four 90-degree angles?

Accepted Answer

Square

Answer

Rectangle

Answer

Rhombus

Question 8

Which shape has opposite sides that are parallel?

Accepted Answer

Parallelogram

Answer

Triangle

Answer

Circle

Answer

Trapezoid

Question 9

If a quadrilateral has two pairs of opposite sides parallel, what type of quadrilateral is it?

Accepted Answer

Parallelogram

Answer

Rectangle

Answer

Trapezoid

Answer

Rhombus

Question 10

Which theorem states that the diagonals of a parallelogram bisect each other?

Accepted Answer

Parallelogram Diagonal Theorem

Answer

Midsegment Theorem

Answer

Pythagorean Theorem

Answer

Triangle Sum Theorem

Question 11

In a rhombus, how are the diagonals?

Accepted Answer

Perpendicular and bisect the angles.

Answer

Perpendicular but do not bisect the angles.

Answer

Bisect the angles but are not perpendicular.

Answer

Neither perpendicular nor bisectors.

Question 12

What is the formula for calculating the area of a trapezoid?

Accepted Answer

½(b₁ + b₂)h

Answer

πr²

Answer

bh

Answer

s²

Question 13

Which theorem relates the diagonals of a rhombus to its sides?

Accepted Answer

Diagonals of a Rhombus Theorem

Answer

Midsegment Theorem

Answer

Pythagorean Theorem

Answer

Triangle Sum Theorem

Question 14

In a rhombus, the diagonals are:

Accepted Answer

Both congruent and perpendicular

Answer

Congruent but not perpendicular

Answer

Perpendicular but not congruent

Answer

Neither congruent nor perpendicular

Question 15

State the theorem that describes the relationship between the diagonals of a parallelogram.

Accepted Answer

Parallelogram Diagonal Theorem

Answer

Angle Bisector Theorem

Answer

Perpendicular Bisector Theorem

Answer

Triangle Angle Sum Theorem

Question 16

Which quadrilateral is characterized by having exactly two parallel sides?

Accepted Answer

Trapezoid

Answer

Rectangle

Answer

Rhombus

Answer

Parallelogram

Question 17

Which type of quadrilateral can be perfectly inscribed within a circle?

Accepted Answer

Cyclic quadrilateral

Answer

Trapezoid

Answer

Rectangle

Answer

Rhombus

Question 18

In a parallelogram, if diagonals AC and BD intersect at point O, which angles are congruent to ∠AOB?

Accepted Answer

Both ∠BOC and ∠AOD

Answer

∠DOC

Answer

∠BOC

Answer

∠AOD

Question 19

Which quadrilateral has opposite sides that are parallel and equal, and opposite angles that are equal?

Accepted Answer

Rectangle

Answer

Trapezoid

Answer

Rhombus

Answer

Kite

Question 20

Which of these shapes is a quadrilateral with all sides equal?

Accepted Answer

Square

Answer

Rectangle

Answer

Rhombus

Answer

Trapezoid

Question 21

Which theorem helps us find the area of a parallelogram?

Accepted Answer

Area of a Parallelogram Theorem

Answer

Pythagorean Theorem

Answer

Area of a Triangle Theorem

Answer

Sine Rule

Question 22

What's the perimeter of a square with a side length of 4 cm?

Accepted Answer

16 cm

Answer

8 cm

Answer

12 cm

Answer

20 cm

Question 23

Which theorem states that the diagonals of a parallelogram bisect each other?

Accepted Answer

Parallelogram Diagonal Bisector Theorem

Answer

Pythagorean Theorem

Answer

Area of a Triangle Theorem

Answer

Angle Bisector Theorem

Question 24

What is the measure of the sum of the interior angles of any quadrilateral?

Accepted Answer

360 degrees

Answer

180 degrees

Answer

270 degrees

Answer

540 degrees

Question 25

What is the area of a square with a side length of 6 cm?

Accepted Answer

36 cm^2

Answer

12 cm^2

Answer

24 cm^2

Answer

48 cm^2

Question 26

Which theorem states that opposite angles of a parallelogram are congruent?

Accepted Answer

Opposite Angles Theorem

Answer

Angle Bisector Theorem

Answer

Quadrilateral Diagonals Theorem

Answer

Parallelogram Diagonals Theorem

Question 27

Which property is NOT true for a parallelogram?

Accepted Answer

All sides are equal.

Answer

Opposite sides are parallel.

Answer

Opposite angles are equal.

Answer

Diagonals bisect each other.

Question 28

If a quadrilateral has four right angles, it is a:

Accepted Answer

Square

Answer

Rhombus

Answer

Trapezoid

Answer

Kite

Question 29

Which theorem states that the diagonals of a parallelogram intersect at their midpoints?

Accepted Answer

Parallelogram Diagonal Theorem

Answer

Pythagorean Theorem

Answer

Converse of the Pythagorean Theorem

Answer

Midsegment Theorem

Question 30

Calculate the perimeter of a square with a side length of 4 inches:

Accepted Answer

16 inches

Answer

8 inches

Answer

12 inches

Answer

20 inches

Question 31

Which theorem can be used to prove that a quadrilateral with opposite angles equal is a parallelogram?

Accepted Answer

Opposite Angles Theorem

Answer

Angle Sum Theorem

Answer

Parallelogram Diagonal Theorem

Answer

Midsegment Theorem

Question 32

A quadrilateral that has two sets of parallel sides is known as a:

Accepted Answer

Parallelogram

Answer

Trapezoid

Answer

Square

Answer

Rectangle

Question 33

What is the total measure of the interior angles in a quadrilateral?

Accepted Answer

360 degrees

Answer

180 degrees

Answer

270 degrees

Answer

540 degrees

Question 34

Which quadrilateral has four right angles?

Accepted Answer

Square

Answer

Trapezoid

Answer

Rhombus

Answer

Parallelogram

Question 35

A quadrilateral with diagonals of equal length is called a:

Accepted Answer

Rhombus

Answer

Rectangle

Answer

Trapezoid

Answer

Parallelogram

Question 36

Which theorem establishes that opposite angles in a parallelogram are congruent?

Accepted Answer

Parallelogram Theorem

Answer

Converse of the Parallelogram Theorem

Answer

Midsegment Theorem

Answer

Trapezoid Theorem

Question 37

Which of the following is NOT a category of trapezoids?

Accepted Answer

Rectangle

Answer

Isosceles

Answer

Scalene

Answer

Right

Question 38

Which type of quadrilateral has two pairs of parallel sides?

Accepted Answer

Parallelogram

Answer

Trapezoid

Answer

Rhombus

Answer

Kite

Question 39

What is the area of a square with side length 6 cm?

Accepted Answer

36 cm²

Answer

12 cm²

Answer

24 cm²

Answer

48 cm²

Question 40

Which theorem states that the sum of the interior angles of any quadrilateral is 360 degrees?

Accepted Answer

Quadrilateral Sum Theorem

Answer

Triangle Sum Theorem

Answer

Exterior Angle Theorem

Answer

Angle Bisector Theorem

Question 41

What is the measure of one interior angle of a regular hexagon?

Accepted Answer

120 degrees

Answer

60 degrees

Answer

108 degrees

Answer

150 degrees

Question 42

Which of the following shapes is a quadrilateral but not a parallelogram?

Accepted Answer

Kite

Answer

Rhombus

Answer

Rectangle

Answer

Square

Question 43

Which quadrilateral has four equal sides and four right angles?

Accepted Answer

Square

Answer

Rectangle

Answer

Rhombus

Answer

Trapezoid

Question 44

Which theorem states that the opposite angles of a parallelogram are equal?

Accepted Answer

Parallelogram Opposite Angles Theorem

Answer

Triangle Sum Theorem

Answer

Pythagorean Theorem

Answer

Converse of the Parallelogram Theorem

Question 45

What is a key characteristic of a trapezoid?

Accepted Answer

One pair of parallel sides

Answer

Two pairs of parallel sides

Answer

No parallel sides

Answer

All sides are equal

Question 46

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a:

Accepted Answer

Parallelogram

Answer

Rectangle

Answer

Rhombus

Answer

Trapezoid

Question 47

Which of the following is NOT a theorem specific to quadrilaterals?

Accepted Answer

Pythagorean Theorem

Answer

Triangle Sum Theorem

Answer

Opposite Sides Theorem

Answer

Parallelogram Diagonal Theorem

Question 48

Which statement is NOT true for all quadrilaterals?

Accepted Answer

They have four right angles.

Answer

They have four sides.

Answer

Opposite sides are parallel.

Answer

Diagonals bisect each other.

Question 49

What type of quadrilateral has four congruent sides and four right angles?

Accepted Answer

Square

Answer

Rectangle

Answer

Parallelogram

Answer

Trapezoid

Question 50

Which theorem states that the diagonals of a rhombus are perpendicular bisectors of each other?

Accepted Answer

Rhombus Diagonal Theorem

Answer

Pythagorean Theorem

Answer

Triangle Congruence Theorem

Answer

Angle Bisector Theorem

Question 51

Find the length of the diagonal of a square with a side length of 4 cm.

Accepted Answer

4√2 cm

Answer

2√2 cm

Answer

8√2 cm

Answer

16√2 cm

Question 52

Which of these theorems CANNOT be used to prove quadrilaterals congruent?

Accepted Answer

Area-Area-Area Congruence

Answer

Side-Side-Side Congruence

Answer

Side-Angle-Side Congruence

Answer

Angle-Side-Angle Congruence

Question 53

Which type of quadrilateral has four equal sides and four right angles?

Accepted Answer

Square

Answer

Rectangle

Answer

Rhombus

Answer

Trapezoid

Question 54

What is the key difference between a parallelogram and a rectangle?

Accepted Answer

Rectangles have right angles, while parallelograms do not.

Answer

Parallelograms have congruent diagonals, while rectangles do not.

Answer

Rectangles are always squares, while parallelograms are not.

Answer

Parallelograms have four equal sides, while rectangles do not.

Question 55

Which theorem is NOT used to prove that a quadrilateral is a parallelogram?

Accepted Answer

Diagonals bisect each other at right angles.

Answer

Opposite sides are congruent.

Answer

Opposite angles are congruent.

Answer

Consecutive angles are supplementary.

Question 56

Which of the following shapes is NOT a quadrilateral?

Accepted Answer

Circle

Answer

Square

Answer

Rectangle

Answer

Trapezoid

Question 57

Which type of quadrilateral has two pairs of parallel sides?

Accepted Answer

Parallelogram

Answer

Rectangle

Answer

Square

Answer

Rhombus

Question 58

What is the measure of an exterior angle of a regular quadrilateral?

Accepted Answer

135 degrees

Answer

90 degrees

Answer

120 degrees

Answer

180 degrees

Question 59

If the diagonals of a parallelogram are perpendicular bisectors of each other, what type of quadrilateral is it?

Accepted Answer

Square

Answer

Rectangle

Answer

Rhombus

Answer

Kite

Question 60

Which of the following is NOT a property of a rectangle?

Accepted Answer

Diagonals are perpendicular bisectors of each other

Answer

Opposite sides are parallel

Answer

Opposite sides are equal

Answer

Opposite angles are equal

Question 61

A quadrilateral with two pairs of parallel sides is called a:

Accepted Answer

Parallelogram

Answer

Trapezoid

Answer

Rhombus

Answer

Square

Question 62

The sum of the interior angles of a quadrilateral is:

Accepted Answer

360 degrees

Answer

180 degrees

Answer

540 degrees

Answer

720 degrees

Question 63

A quadrilateral with four equal sides is called a:

Accepted Answer

Square

Answer

Rectangle

Answer

Rhombus

Answer

Parallelogram

Question 64

Which theorem states that the opposite angles of a parallelogram are congruent?

Accepted Answer

Opposite Angles Theorem

Answer

Angle Sum Theorem

Answer

Parallel Lines Theorem

Answer

Triangle Inequality Theorem