MM1G3.d

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# MM1G3.d - PowerPoint PPT Presentation

Parallelograms. MM1G3.d. B. C. D. A. Parallelogram. Definition:. A quadrilateral whose opposite sides are parallel. A parallelogram is named using all four vertices. You can start from any one vertex, but you must continue in a clockwise or counterclockwise direction.

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B

C

D

A

Parallelogram

Definition:

A quadrilateral whose opposite sides are parallel.

• A parallelogram is named using all four vertices.
• You can start from any one vertex, but you must continue in a clockwise or counterclockwise direction.
• For example, the figure above can be either ABCD or ADCB.

Symbol:

a smaller version

of a parallelogram

Naming:

A

B

Properties of Parallelogram

P

D

C

1. Both pairs of opposite sides are congruent.

2. Both pairs of opposite angles are congruent.

3. Consecutive angles are supplementary.

4. Diagonals bisect each other but are not congruent

P is the midpoint of .

H

K

Examples

M

P

L

• Draw HKLP.
• HK = _______ and HP = ________ .
• m<K = m<______ .
• m<L + m<______ = 180.
• If m<P = 65, then m<H = ____,m<K = ______ and m<L =____.
• Draw the diagonals with their point of intersection labeled M.
• If HM = 5, then ML = ____ .
• If KM = 7, then KP = ____ .
• If HL = 15, then ML = ____ .
• If m<HPK = 36, then m<PKL = _____ .

PL

KL

P

P or K

115°

115°

65

5 units

14 units

7.5 units

36;

(Alternate interior angles are congruent.)