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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.