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Identify Parallelograms
Determine whether the quadrilateral is a parallelogram. Justify your answer.
Answer: Each pair of opposite sides has the same measure. Therefore, they are congruent.If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram.
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A. Both pairs of opp. sides ||.
B. Both pairs of opp. sides .
C. Both pairs of opp. s .
D. One pair of opp. sides both || and .
Which method would prove the quadrilateral is a parallelogram?
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Use Parallelograms to Prove Relationships
MECHANICS Scissor lifts, like the platform lift shown, are commonly applied to tools intended to lift heavy items. In the diagram, A C and B D. Explain why the consecutive angles will always be supplementary, regardless of the height of the platform.
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Use Parallelograms to Prove Relationships
Answer: Since both pairs of opposite angles of quadrilateral ABCD are congruent, ABCD is a parallelogram by Theorem 6.10. Theorem 6.5 states that consecutive angles of parallelograms are supplementary. Therefore, mA + mB = 180 and mC + mD = 180. By substitution, mA + mD = 180 and mC + mB = 180.
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The diagram shows a car jack used to raise a car from the ground. In the diagram, AD BC and AB DC. Based on this information, which statement will be true, regardless of the height of the car jack.
A. A B
B. A C
C. AB BC
D. mA + mC = 180
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Use Parallelograms and Algebra to Find Values
Find x and y so that the quadrilateral is a parallelogram.
Opposite sides of a parallelogram are congruent.
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Use Parallelograms and Algebra to Find Values
Substitution
Distributive Property
Add 1 to each side.
Subtract 3x from each side.
AB = DC
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Use Parallelograms and Algebra to Find Values
Answer: So, when x = 7 and y = 5, quadrilateral ABCD is a parallelogram.
Substitution
Distributive Property
Add 2 to each side.
Subtract 3y from each side.
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Parallelograms and Coordinate Geometry
COORDINATE GEOMETRY Quadrilateral QRST has vertices Q(–1, 3), R(3, 1), S(2, –3), and T(–2, –1). Determine whether the quadrilateral is a parallelogram. Justify your answer by using the Slope Formula.
If the opposite sides of a quadrilateral are parallel, then it is a parallelogram.
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Parallelograms and Coordinate Geometry
Answer: Since opposite sides have the same slope, QR║ST and RS║TQ. Therefore, QRST is a parallelogram by definition.
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A. yes
B. no
Graph quadrilateral EFGH with vertices E(–2, 2), F(2, 0), G(1, –5), and H(–3, –2). Determine whether the quadrilateral is a parallelogram.