Parallelograms
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Parallelograms. B. C. D. A. Parallelogram. Definition:. A quadrilateral with both pairs of opposite sides parallel. The symbol for parallelogram is a smaller version of the figure. A parallelogram is named using all four vertices.

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Parallelograms

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Parallelograms

Parallelograms


Parallelogram

B

C

D

A

Parallelogram

Definition:

A quadrilateral with both pairs of opposite sides parallel.

  • The symbol for parallelogram is a smaller version of the figure.

  • 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.


Properties of parallelogram

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. Diagonals bisect each other but are not congruent

P is the midpoint of AC and BD, so BP = PD and AP = PC.


Examples

H

Examples

K

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°

65°

115°

5 units

(Alternate interior

angles are congruent.)

14 units

7.5 units

36°


Examples1

Examples

  • ABCD is a parallelogram. Find the values of x, y, and z.


Parallelograms 3312677

Example 2: In GEOM, EA = 2x2 + 5x and AM = 4x + 2. Find the value of x. What are EA and AM?

G

M

A

E

O


Parallelograms 3312677

Example 3. Given TRAC. If TC = 3x - 5 and RA = 25, solve for x.

T

R

3

4

K

1

2

If m∠CTR = 2y - 13 and m∠ACT = y + 1. Find y.

C

A


Example 4

Example 4


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