11.1 Parallelograms

CCSS

Content Standards
G.CO.11 Prove theorems about
parallelograms.
G.GPE.4 Use coordinates to prove simple
geometric theorems algebraically.
Mathematical Practices
4 Model with mathematics.
3 Construct viable arguments and critique the reasoning of others.

Then/Now

You classified polygons with four sides as
quadrilaterals.

• Recognize and apply properties of the sides

and angles of parallelograms.

• Recognize and apply properties of the

diagonals of parallelograms.

Concept 1

​Congruent sides

​Congruent angles

​Supp
Angles

Example 1A

Use Properties of Parallelograms

A. In parallelogram ABCD suppose
m∠B = 32, CD = 80 inches, BC = 15 inches.
Find AD.

Answer:AD = 15 inches

Multiple Choice

ABCD is a parallelogram. Find AD.

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Example 1B

Use Properties of Parallelograms

Answer:m∠C = 148

B. In parallelogram ABCD suppose
m∠B = 32, CD = 80 inches, BC = 15 inches.
Find m∠C.

Multiple Choice

ABCD is a parallelogram. Find $$m\angle D.$$

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• 54

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• 154

Example 1C

Use Properties of Parallelograms

C. In parallelogram ABCD suppose
m∠B = 32, CD = 80 inches, BC = 15 inches.
Find m∠D.

Answer:m∠D = 32

• Opposite angles are CONGRUENT (this means EQUAL).

• Item

Multiple Choice

ABCD is a parallelogram. Find $$m\angle C.$$

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• 54

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• 154

Concept 3

Example 2A

Use Properties of Parallelograms and Algebra

A. If WXYZ is a parallelogram, find the value of r.

Opposite sides of a
parallelogram are ≅.

Substitution

Divide each side by 4.

Answer:r = 4.5

​Set the opposite sides equal in an equation and solve for r.

Multiple Choice

ABCD is a parallelogram. Find p.

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Example 2B

Use Properties of Parallelograms and Algebra

B. If WXYZ is a parallelogram, find the value of s.

8s =

7s + 3

Diagonals of a parallelogram bisect each other.

Answer: s = 3

s

=

3

Subtract 7s from each side.

​To bisect is to cut in half. Set up an equation with one side of the diagonal equal to the other.

Multiple Choice

ABCD is a parallelogram. Find the value of x.

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​YES!! Opposite sides are congruent.

​YES!! Diagonals bisect each other.

​YES!! Consecutive angles are supplementary.

Assignments to Practice Skill

​IXL O.6 & O.7 Parallelograms

Using this lesson and the properties, complete the IXL. If you miss a problem, take the time to read the explanation provided. This is a self taught lesson, make sense of it!!

2/9 complete to 60 SS
5/8 complete to 80 SS