Concept 1
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Transcript of Concept 1
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Use Properties of Parallelograms
A. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find AD.
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Use Properties of Parallelograms
AD = BC Opposite sides of a are .
= 15 Substitution
Answer: AD = 15 inches
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Use Properties of Parallelograms
B. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find mC.
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Use Properties of Parallelograms
Answer: mC = 148
mC + mB = 180 Cons. s in a are supplementary.
mC + 32 = 180 Substitution
mC = 148 Subtract 32 from each side.
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Use Properties of Parallelograms
C. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find mD.
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Use Properties of Parallelograms
Answer: mD = 32
mD = mB Opp. s of a are .
= 32 Substitution
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Use Properties of Parallelograms and Algebra
A. If WXYZ is a parallelogram, find the value of r.
Opposite sides of a parallelogram are .
Definition of congruence
Substitution
Divide each side by 4.Answer: r = 4.5
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Use Properties of Parallelograms and Algebra
B. If WXYZ is a parallelogram, find the value of s.
8s = 7s + 3 Diagonals of a bisecteach other.
Answer: s = 3
s = 3 Subtract 7s from each side.
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Use Properties of Parallelograms and Algebra
C. If WXYZ is a parallelogram, find the value of t.
ΔWXY ΔYZW Diagonal separates a parallelogram into
2 triangles.
YWX WYZ CPCTC
mYWX = mWYZ Definition of congruence
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Use Properties of Parallelograms and Algebra
2t = 18 Substitution
t = 9 Divide each side by 2.
Answer: t = 9
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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)?
Since the diagonals of a parallelogram bisect each other, the intersection point is the midpoint of
Find the midpoint of
Midpoint Formula
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Parallelograms and Coordinate Geometry
Answer: The coordinates of the intersection of the diagonals of parallelogram MNPR are (1, 2).