Students will describe & apply properties (AKA Theorems) to identify & prove quadrilaterals are parallelograms.

Why? So you can describe how a music stand works, as seen in Ex 32.

Mastery is 80% or better on 5-minute checks and practice problems.

When the opposite sides of a flat shape are parallel and of the same length, it can be correctly labeled as a parallelogram. Additionally, the opposite angles in a parallelogram are always equal to each other. According to this definition, rectangles, rhombuses, and even squares are parallelograms. Examples of parallelograms are often seen in everyday life hiding in the most obvious places. Any item that is rectangular, like a door, TV, or book, is a type of parallelogram. The same goes for any square-shaped object. Also, used in engineering ,for machines that need to lift heavy objects, lifting cars, lifting big shovels, in design like architecture and also in ergonomic design of furniture etc.

Theorem 8.7: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

A

D

B

C

ABCD is a parallelogram.

Theorem 8.8: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

A

D

B

C

ABCD is a parallelogram.

Theorem 8.5: If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.

A

D

B

C

ABCD is a parallelogram.

x°

(180 – x)° x°

Theorem 8.10: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

ABCD is a parallelogram.

A

D

B

C

With Common Core here, it is more about what you can prove as opposed to what you know.

In a short paragraph, explain everything you know about parallelograms. Be prepared to share out.

Great…..you just named all the criteria (proof) you will need to prove a quadrilateral is a parallelogram on your next performance task.

Students will describe & apply properties to identify & prove quadrilaterals are parallelograms.

• Show that both pairs of opposite sides are parallel.• Show that both pairs of opposite sides are congruent.• Show that both pairs of opposite angles are congruent.• Show that one angle is supplementary to both consecutive

angles.• Show that the diagonals bisect each other.• Show that one pair of opposite sides are congruent and

parallel.

In a short paragraph, list all the ways you would be able to prove a quadrilateral is a parallelogram.

Students will describe & apply properties to identify parallelograms.

Why? So you can describe how a music stand works, as seen in Ex 32.

Mastery is 80% or better on 5-minute checks and practice problems.

.Remember all PowerPoints are online as well as the book.

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Quiz Tomorrow 8.1-8.3