6.2 Parallelograms

CCSS

Content StandardsG.CO.11 Prove theorems about parallelograms.G.GPE.4 Use coordinates to prove simple geometric theorems algebraically.Mathematical Practices4 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.

Vocabulary

• Parallelogram:

a quadrilateral with both pairs of opposite sides parallel

VocabularyTheorem 6.3: Parallelogram Property #1If a quadrilateral is a parallelogram, then

its opposite sides are congruent.

VocabularyTheorem 6.4: Parallelogram Property #2If a quadrilateral is a parallelogram, then

its opposite angles are congruent.

VocabularyTheorem 6.5: Parallelogram Property #3If a quadrilateral is a parallelogram, then

its consecutive angles are supplementary.

VocabularyTheorem 6.6: Parallelogram Property #4If a parallelogram has one right angle,

then it has four right angles.

VocabularyTheorem 6.7: Parallelogram Diagonal Property #1

If a quadrilateral is a parallelogram, then its diagonals bisect each other.

VocabularyTheorem 6.8: Parallelogram Diagonal Property #2

If a quadrilateral is a parallelogram, then each diagonal separates the parallelogram into two congruent triangles.

Parallelogram

• Mark in all of the sides and angles

Example 1A

A. 10

B. 20

C. 30

D. 50

A. ABCD is a parallelogram. Find AB.

Example 1B

A. 36

B. 54

C. 144

D. 154

B. ABCD is a parallelogram. Find mC.

Example 1C

A. 36

B. 54

C. 144

D. 154

C. ABCD is a parallelogram. Find mD.

Example 1AUse Properties of Parallelograms

A. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find AD.

Example 1BUse Properties of Parallelograms

B. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find mC.

Example 1CUse Properties of Parallelograms

C. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find mD.

Example 2AUse Properties of Parallelograms and Algebra

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

Example 2BUse Properties of Parallelograms and Algebra

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

Example 2CUse Properties of Parallelograms and Algebra

C. If WXYZ is a parallelogram, find the value of t.

Example 2A

A. 2

B. 3

C. 5

D. 7

A. If ABCD is a parallelogram, find the value of x.

Example 2B

A. 4

B. 8

C. 10

D. 11

B. If ABCD is a parallelogram, find the value of p.

Example 2C

A. 4

B. 5

C. 6

D. 7

C. If ABCD is a parallelogram, find the value of k.

Example 3Parallelograms and Coordinate Geometry

What are the coordinates of the intersection of the diagonals of parallelogram MNPR, with vertices M(–3, 0), N(–1, 3), P(5, 4), and R(3, 1)?

Example 3What are the coordinates of the intersection of the diagonals of parallelogram LMNO, with verticesL(0, –3), M(–2, 1), N(1, 5), O(3, 1)?

Parallelograms and Coordinate Geometry