5.6 Proving That a Quadrilateral is a Parallelogram Objective: After studying this section, you will...

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5.6 Proving That a Quadrilateral is a Parallelogram Objective: After studying this section, you will be able to prove that a quadrilateral is a parallelogram.

Transcript of 5.6 Proving That a Quadrilateral is a Parallelogram Objective: After studying this section, you will...

Page 1: 5.6 Proving That a Quadrilateral is a Parallelogram Objective: After studying this section, you will be able to prove that a quadrilateral is a parallelogram.

5.6 Proving That a Quadrilateral is a

ParallelogramObjective:

After studying this section, you will be able to prove that a quadrilateral is a

parallelogram.

Page 2: 5.6 Proving That a Quadrilateral is a Parallelogram Objective: After studying this section, you will be able to prove that a quadrilateral is a parallelogram.

Methods to prove quadrilateral ABCD is a parallelogram

1. If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram (reverse of the definition).

A B

D C

2. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram (converse of a property).

Page 3: 5.6 Proving That a Quadrilateral is a Parallelogram Objective: After studying this section, you will be able to prove that a quadrilateral is a parallelogram.

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

4. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram (converse of a property).

5. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram (converse of a property).

Page 4: 5.6 Proving That a Quadrilateral is a Parallelogram Objective: After studying this section, you will be able to prove that a quadrilateral is a parallelogram.

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Given: ACDF is a parallelogram

Prove: FBCE is a parallelogram

C

E

A

DF

B

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AFB ECD

Page 5: 5.6 Proving That a Quadrilateral is a Parallelogram Objective: After studying this section, you will be able to prove that a quadrilateral is a parallelogram.

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Given:

C K

A

R

B

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AC BK

C K

is isosceles, with base CAR CR

Prove: BARK is a parallelogram

Page 6: 5.6 Proving That a Quadrilateral is a Parallelogram Objective: After studying this section, you will be able to prove that a quadrilateral is a parallelogram.

Given: Quadrilateral QUAD with angles as shown

Show that QUAD is a parallelogram UA

QD

52x

10x 23 5x x x

3 23 15x x

Page 7: 5.6 Proving That a Quadrilateral is a Parallelogram Objective: After studying this section, you will be able to prove that a quadrilateral is a parallelogram.

Given: NRTW is a parallelogram

Prove: XPSV is a parallelogram

R

T

N

W V

S

P

X

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NX TS

WV PR

Page 8: 5.6 Proving That a Quadrilateral is a Parallelogram Objective: After studying this section, you will be able to prove that a quadrilateral is a parallelogram.

Summary

Using one of the methods to prove quadrilaterals are parallelograms, create your own problem and show how it is a parallelogram.

Homework: worksheet


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