View by Category

The presentation will start after a short

(15 second) video ad from one of our sponsors.

Hot tip: Video ads won’t appear to registered users who are logged in. And it’s free to register and free to log in!

(15 second) video ad from one of our sponsors.

Hot tip: Video ads won’t appear to registered users who are logged in. And it’s free to register and free to log in!

Loading...

PPT – Parallelograms PowerPoint presentation | free to download - id: 5be12-ODUxZ

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

Parallelograms

Quadrilaterals are four-sided polygons

Parallelogram is a quadrilateral with both pairs

of opposite sides parallel.

Parallelograms (2)

A

B

D

C

Theorem 6.1 Opposite sides of a parallelograms

are congruent

AD ? BC and AB ? DC

Theorem 6.2 Opposite angles of a parallelogram

are congruent

ltA ? ltC and ltB ? ltD

mltAmltB 180 m ltBmltC 180 mltCmltD

180 mltDmltA 180

Theorem 6.3 Consecutive angles in a

parallelogram are supplementary.

Parallelograms (3)

Diagonals of a figure Segments that connect any

to vertices of a polygon

A

B

Theorem 6.4 The diagonals of a parallelogram

bisect each other.

D

C

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?

Tests for Parallelograms

Theorem 6.5 If both pairs of opposite sides of a

quadrilateral are congruent, then the

quadrilateral is a parallelogram.

A

B

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

parallelogram

D

C

Theorem 6.6 If both pairs of opposite angles of

a quadrilateral are congruent, then the

quadrilateral is a parallelogram.

If ltA ? ltC and ltB ? ltD, then ABCD is a

parallelogram

Tests for Parallelograms 2

Theorem 6.7 If the diagonals of a quadrilateral

bisect each other, then the quadrilateral is a

parallelogram

A

B

D

C

Theorem 6.8 If one pair of opposite sides of a

quadrilateral is both parallel and congruent,

then the quadrilateral is a parallelogram.

A quadrilateral is a parallelogram if...

Both pairs of opposite sides are parallel.

(Definition)

Both pairs of opposite sides are congruent.

(Theorem 6.5)

Both pairs of opposite angles are congruent.

(Theorem 6.6)

Diagonals bisect each other. (Theorem 6.7)

A pair of opposite sides is both parallel and

congruent. (Theorem 6.8)

Area of a parallelogram

If a parallelogram has an area of A square units,

a base of b units and a height of h units, then A

bh. (Do example 1 p. 530)

h

b

The area of a region is the sum of the areas of

all its non-overlapping parts. (Do example 3 p.

531)

Rectangles

A rectangle is a quadrilateral with four right

angles.

Opp. angles in rectangles are congruent (they

are right angles) therefore rectangles are

parallelograms with all their properties.

Theorem 6-9 If a parallelogram is a rectangle,

then its diagonals are

congruent.

Theorem 6-10 If the diagonals of a

parallelogrma are congruent then the

parallelogram is a rectangle.

Rectangles (2)

- If a quadrilateral is a rectangle, then the

following properties hold true - Opp. Sides are congruent and parallel
- Opp. Angles are congruent
- Consecutive angles are supplementary
- Diagonals are congruent and bisect each other
- All four angles are right angles

Squares and Rhombi

A rhombus is a quadrilateral with four congruent

sides. Since opp. sides are ? , a rhombus is a

parallelogram with all its properties.

Special facts about rhombi Theorem 6.11 The

diagonals of a rhombus are

perpendicular. Theorem 6.12 If the diagonals of

a parallelogram are perpendicular, then

the parallelogram is a

rhombus. Theorem 6.13 Each diagonal of a rhombus

bisects a pair of opp.

angles

C

Squares and Rhombi(2)

If a rhombus has an area of A square units and

diagonals of d1 and d2 units, then A ½ d1d2.

If a quadrilateral is both, a rhombus and a

rectangle, is a square

Area of a triangle

h

b

If a triangle has an area of A square units a

base of b units and corresponding height of h

units, then A ½bh.

Congruent figures have equal areas.

Trapezoids

A trapezoid is a quadrilateral with exactly one

pair of parallel sides. The parallel sides are

called bases. The nonparallel sides are called

legs. At each side of a base there is a pair of

base angles.

C

Trapezoids (2)

A

B

AB base CD base AC leg BD leg

AB ?? CD AC BD are non parallel

C

D

ltA ltB pair of base angles ltC ltD pair of

base angles

C

Trapezoids (3)

Isosceles trapezoid A trapezoid with congruent

legs. Theorem 6-14 Both pairs of base angles of

an isosceles trapezoid are congruent. Theorem

6-15 The diagonals of an isosceles trapezoid are

congruent.

Trapezoids (4)

The median of a trapezoid is the segment that

joints the midpoints of the legs (PQ).

A

B

Q

P

C

D

Theorem 6-16 The median of a trapezoid is

parallel to the bases, and its measure is

one-half the sum of the measures of its bases.

C

Area of Trapezoids

B

A

h

C

D

Area of a trapezoid If a trapezoid has an area

of A square units, bases of b1 and b2 units and

height of h units, then A ½(b1 b2 )h.

C

This powerpoint was kindly donated to

www.worldofteaching.com http//www.worldofteac

hing.com is home to over a thousand powerpoints

submitted by teachers. This is a completely free

site and requires no registration. Please visit

and I hope it will help in your teaching.

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

Page of

CrystalGraphics Sales Tel: (800) 394-0700 x 1 or Send an email

Home About Us Terms and Conditions Privacy Policy Contact Us Send Us Feedback

Copyright 2017 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2017 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Parallelograms" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!