5.9 Show that a Quadrilateral is a Parallelogram wooo hoooâ¦get excitedâ¦oh yea!!!!

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# 5.9 Show that a Quadrilateral is a Parallelogram wooo hoooâ¦get excitedâ¦oh yea!!!! - PowerPoint PPT Presentation

5.9 Show that a Quadrilateral is a Parallelogram wooo hooo…get excited…oh yea!!!!. Theorems of Quadrilaterals. 5.22 If both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram. (draw what’s needed on the diagram to make it fit the theorem)

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### 5.9Show that a Quadrilateral is a Parallelogramwooo hooo…get excited…oh yea!!!!

5.22 If both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram.(draw what’s needed on the diagram to make it fit the theorem)

5.23 If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram.(draw what’s needed on the diagram to make it fit the theorem)

5.24 If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram. (draw what’s needed on the diagram to make it fit the theorem)

5.25 If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. (draw what’s needed on the diagram to make it fit the theorem)

ALGEBRA

Find the values of xand y.

CD

AB=

Opposite sides of a are .

12

x + 4=

x =

8

or m A = m C.

By Theorem 8.4, A C,

InABCD, x = 8andy = 65.

ABCDis a . Use parallelogram by the definition of a parallelogram Theorem 8.3 to find the value of x.

Substitute x + 4 for ABand 12 for CD.

Subtract 4 from each side.

So, y ° = 65°.

Find FGand m G.

Find the values of xand y.

1.

2.

8, 60°

25, 15

GUIDEDPRACTICE

Find the indicated measure in JKLM.

6.

3.

4.

5.

NM

m KML

KM

m JML

4

70°

40°

2