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Slide 1

Quadrilaterals are four-sided polygons

Parallelogram: is a quadrilateral with both pairs of opposite sides parallel.

Slide 2

Parallelograms (2)

Theorem 6.1 : Opposite sides of a parallelograms are congruent

Theorem 6.2: Opposite angles of a parallelogram are congruent

Theorem 6.3: Consecutive angles in a parallelogram

are supplementary.

A

D

C

B

AD BC and AB DC

<A <C and <B <D

m<A+m<B = 180°

m <B+m<C = 180°

m<C+m<D = 180°

m<D+m<A = 180°

Slide 3

Parallelograms (3)

Diagonals of a figure: Segments that connect any to vertices of a polygon

Theorem 6.4: The diagonals of a parallelogram bisect each other.

A

B

C

D

Slide 4

Parallelograms (4)

Draw a parallelogram : ABCD on a piece of construction paper.

Cut the parallelogram.

Fold the paper and make a crease from A to C and from B to D.

Fold the paper so A lies on C. What do you observe?

Fold the paper so B lies on D. What do you observe?

What theorem is confirmed by these Observations?

Slide 5

Theorem 6.5 :If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Theorem 6.6: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

A

D

C

B

If AD BC and AB DC, then ABCD is a parallelogram

If <A <C and <B <D, then ABCD is a parallelogram

Slide 6

Tests for Parallelograms 2

Theorem 6.7: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram

A

D

C

B

Theorem 6.8: If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram.

Slide 7

Diagonals bisect each other. (Theorem 6.7)

A pair of opposite sides is both parallel and congruent. (Theorem 6.8)

Both pairs of opposite sides are congruent. (Theorem 6.5)

Both pairs of opposite angles are congruent. (Theorem 6.6)

Both pairs of opposite sides are parallel. (Definition)

Slide 8

- Parallelograms
- Tests for Parallelograms
- A quadrilateral is a parallelogram if .
- Area of a parallelogram
- Rectangles
- Squares and Rhombi
- Area of a triangle
- Trapezoids
- Area of Trapezoids

- Understanding Heat Transfer, Conduction, Convection and Radiation
- Static and Kinetic Friction
- Solar Thermal Energy
- Solar Energy
- Newton’s Law of Gravity
- Direct heat utilization of geothermal energy
- Waves & Sound

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