Properties of Parallelograms. What is a Parallelogram? A Quadrilateral with two sets of parallel sides.

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Presentation transcript:

Properties of Parallelograms

What is a Parallelogram? A Quadrilateral with two sets of parallel sides.

5 Properties of Parallelograms 1. Parallelograms have two sets of parallel sides (definition) 2. Opposite sides of a parallelogram are congruent 3. Opposite angles of a parallelogram are congruent 4. Consecutive angles of a parallelogram are supplementary 5. The diagonals of a parallelogram bisect each other. What is a diagonal? A line connecting opposite angles of a polygon.

Properties of Parallelograms

Using the properties of parallelograms The shape below is a parallelogram. Find x and y. 68x y+12 The angle with x and the angle with 68 are consecutive angles. Therefore we know they are supplementary and can write: x + 68 = 180. x = 112 The angle with 68 and the angle with y + 12 are opposite angles. Therefore we know they are congruent. y + 12 = 68 y = 56

Using the properties of parallelograms The shape below is a parallelogram. Find x. 7x-1 6x+2 2x+410 There are to equations you can use to solve for x. The important fact is that opposite sides are congruent. The sides 10 and 2x+4 are opposite so you can write 10=2x+4. Also, the sides 7x-1 and 6x+2 are opposite so you can write 7x-1=6x+2. Both of the equations have answers of x=3.

Using the properties of parallelograms The shape below is a parallelogram. Find x and y. 75 x y 42 z x = 105, y = 33, z = 33

HOMEWORK Pg. 297 (1-21 odd, 34,35,39-41,47-50)

Proving the Properties of Parallelograms – (Honors Geometry) Prove the opposite sides of a parallelogram are congruent. STATEMENTSREASONS. Given: AB ll CD BC ll DA Prove: AB = CD BC =DA

Open Textbook to Page 300 (56-60) Q: Why does your math textbook have such a hard life? A: It has way to many problems.

Additional Honors Homework Pg. 300 (51,52,56-60)