Five-Minute Check (over Lesson 6–1)

Then/Now

New Vocabulary

Theorems: Properties of Parallelograms

Proof: Theorem 6.4

Example 1: Real-World Example: Use Properties of Parallelograms

Theorems: Diagonals of Parallelograms

Example 2: Use Properties of Parallelograms and Algebra

Example 3: Parallelograms and Coordinate Geometry

Example 4: Proofs Using the Properties of Parallelograms

Over Lesson 6–1

A. 180

B. 162

C. 144

D. 126

Find the measure of an interior angle of a regular polygon that has 10 sides.

Over Lesson 6–1

A. 135

B. 150

C. 165

D. 180

Find the measure of an interior angle of a regular polygon that has 12 sides.

Over Lesson 6–1

A. 3600

B. 3420

C. 3240

D. 3060

What is the sum of the measures of the interior angles of a 20-gon?

Over Lesson 6–1

A. 3060

B. 2880

C. 2700

D. 2520

What is the sum of the measures of the interior angles of a 16-gon?

Over Lesson 6–1

A. 21

B. 15.25

C. 12

D. 10

Find x if QRSTU is a regular pentagon.

Over Lesson 6–1

A. pentagon

B. hexagon

C. octagon

D. decagon

What type of regular polygon has interior angles with a measure of 135 ?

You classified polygons with four sides as quadrilaterals. (Lesson 1–6)

• Recognize and apply properties of the sides and angles of parallelograms.

• Recognize and apply properties of the diagonals of parallelograms.

• parallelogram

Use Properties of Parallelograms

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

Use Properties of Parallelograms

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

Use Properties of Parallelograms

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

A. 10

B. 20

C. 30

D. 50

A. ABCD is a parallelogram. Find AB.

A. 36

B. 54

C. 144

D. 154

B. ABCD is a parallelogram. Find mC.

A. 36

B. 54

C. 144

D. 154

C. ABCD is a parallelogram. Find mD.

Use Properties of Parallelograms and Algebra

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

Use Properties of Parallelograms and Algebra

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

Use Properties of Parallelograms and Algebra

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

A. 2

B. 3

C. 5

D. 7

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

A. 4

B. 8

C. 10

D. 11

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

A. 4

B. 5

C. 6

D. 7

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

Parallelograms 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)?

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

A.

B.

C.

D.