Properties of Parallelograms

Properties of Parallelograms

Geometry CP - Ms. Aiken

Parallelograms

A parallelogram is a quadrilateral with 2 pairs of parallel sides.

Properties of Parallelograms - 1 of 4

Opposite Angles Theorem: If a quadrilateral is a parallelogram, then both pairs of opposite angles are congruent.

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Example: If <B measures 85 degrees,

<D also measures 85 degrees.

Properties of Parallelograms - 1 of 4

Opposite Angles Theorem: If a quadrilateral is a parallelogram, then both pairs of opposite angles are congruent.

Example with algebra:

​m<B = m<D

x + 25 = 85

-25 -25

x = 60

Multiple Choice

A _______________ is a quadrilateral with two sets of parallel sides.

• trapezoid

• parallelogram

• kite

• triangle

Multiple Choice

The opposite angles of a parallelogram are ...

• complementary

• congruent

• supplementary

• perpendicular

Multiple Choice

Find x.

• 82

• 92

• 98

• 102

Properties of Parallelograms - 2 of 4

Consecutive Angles Theorem: If a quadrilateral is a parallelogram, then all pairs of consecutive angles are supplementary.

Vocabulary: Consecutive -> next to each other, on the same side

Supplementary -> sum = 180 degrees

Example) B + C = 180

A + D = 180

Properties of Parallelograms - 2 of 4

Consecutive Angles Theorem: If a quadrilateral is a parallelogram, then all pairs of consecutive angles are supplementary.

Example

​If <A = 70, then <B = 110 because

70 + 110 = 180.

Properties of Parallelograms - 2 of 4

Consecutive Angles Theorem: If a quadrilateral is a parallelogram, then all pairs of consecutive angles are supplementary.

Example 2

m<X + m<Y = 180

(c - 20) + (c - 30) = 180

2c - 50 = 180

+50 +50

2c = 230

/2 /2

c = 115

Multiple Choice

In a parallelogram, consecutive angles are __________.

• congruent

• supplementary

• corresponding

• parallel

Multiple Choice

Find x.

• 75

• 85

• 105

• 95

Multiple Choice

Solve for x. Each figure is a parallelogram.

• A

• B

• C

• D

Properties of Parallelograms - 3 of 4

Opposite Sides Theorem: If a quadrilateral is a parallelogram, then both pairs of opposite sides are congruent.

Example) If side AD = 8 cm,

then side BC = 8cm.

Properties of Parallelograms - 3 of 4

Opposite Sides Theorem: If a quadrilateral is a parallelogram, then both pairs of opposite sides are congruent.

AB = DC

5x - 8 = 2x + 13

+ 8 +8

5x = 2x + 21

-2x -2x

3x = 21

/3 /3

x = 7

Multiple Choice

The opposite sides of a parallelogram are congruent.

• true

• false

• maybe

• sometimes

Multiple Choice

Find the measurement indicated in each parallelogram.

• A

• B

• C

• D

Multiple Choice

Solve for x. Each figure is a parallelogram.

• A

• B

• C

• D

Properties of Parallelograms - 4 of 4

Parallelogram Diagonals Theorem: If a quadrilateral is a parallelogram, then the diagonals bisect each other.

***Remember, bisect means to cut in half. Each half is equal to the other.

Properties of Parallelograms - 4 of 4

Parallelogram Diagonals Theorem: If a quadrilateral is a parallelogram, then the diagonals bisect each other

Example:

Multiple Choice

In a parallelogram, diagonals are __________.

• perpendicular

• bisected

• congruent

• parallel

Multiple Choice

If ABCD is a parallelogram, what is the length of ED? 

• 10

• 11

• 7

• 5

Multiple Choice

If ABCD is a parallelogram, what is the length of BD? 

• 10

• 11

• 7

• 5

Multiple Choice

Which is NOT a property of a parallelogram?

• Diagonals bisect each other

• Diagonals are congruent

• Both pairs of opposite sides are parallel

• Both pairs of opposite angles are congruent