Lesson 61 Determining if a Quadrilateral is a Parallelogram

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Objective: Prove that a given quadrilateral is a parallelogram. 6.3 Proving Quadrilaterals are Parallelograms Handbook, p. 19.

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Presentation transcript:

Lesson 61 Determining if a Quadrilateral is a Parallelogram Properties of sides, diagonals and angles of parallelograms.

What are some properties of parallelograms? From Lesson 34 we learned: Opposite sides parallel Opposite sides congruent Opposite angles congruent Consecutive angles supplementary Diagonals bisect each other

“Converse” of Lesson 34 You will be using the converse of some of those properties to prove if a quadrilateral is a parallelogram.

Identifying Parallelograms If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Identifying Parallelograms If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Find x, y, & z that would make ABCD a parallelogram. 8𝑥−70=3𝑥+5 5𝑥=75 𝑥=15 7𝑦=9𝑦−32 −2𝑦=−32 𝑦=16 7 16 +4𝑧=180 112+4𝑧=180 4𝑧=68 𝑧=17

Identifying Parallelograms If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram.

Identifying Parallelograms If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Is quadrilateral JKLM a parallelogram? 5𝑥−24=26 5𝑥=50 x=10 2 10 =10+10 20=20 4 10 −5=2 10 +15 35=35 Yes, diagonals bisect each other.

Remember use these properties to prove a quadrilateral is a parallelogram Opposite sides congruent Opposite angles congruent Diagonals bisect each other One pair parallel & congruent Any questions?