6-3 Proving that a Quadrilateral is a Parallelogram Objective: To determine whether a quadrilateral...

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6-3 Proving that a Quadrilateral is a Parallelogram Objective: To determine whether a quadrilateral is a parallelogram Essential Understanding: You can decide whether a quadrilateral is a parallelogram if its sides, angles and diagonals have certain properties

Transcript of 6-3 Proving that a Quadrilateral is a Parallelogram Objective: To determine whether a quadrilateral...

Page 1: 6-3 Proving that a Quadrilateral is a Parallelogram Objective: To determine whether a quadrilateral is a parallelogram Essential Understanding: You can.

6-3Proving that a

Quadrilateral is a Parallelogram

Objective: To determine whether a quadrilateral is a parallelogram

Essential Understanding: You can decide whether a quadrilateral is a parallelogram if its sides, angles and diagonals have certain properties

Page 2: 6-3 Proving that a Quadrilateral is a Parallelogram Objective: To determine whether a quadrilateral is a parallelogram Essential Understanding: You can.

Opposite angles are congruent

Review

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent

Consecutive angles are supplementary

Diagonals bisect each other

Page 3: 6-3 Proving that a Quadrilateral is a Parallelogram Objective: To determine whether a quadrilateral is a parallelogram Essential Understanding: You can.

Theorems 6-9 and 6-10 are the converses of Theorems 6-4 and 6-5, respectively. They use angle relationships to conclude that a quadrilateral is a parallelogram.

Page 4: 6-3 Proving that a Quadrilateral is a Parallelogram Objective: To determine whether a quadrilateral is a parallelogram Essential Understanding: You can.
Page 5: 6-3 Proving that a Quadrilateral is a Parallelogram Objective: To determine whether a quadrilateral is a parallelogram Essential Understanding: You can.

Example:

For what value of y must PQRS be a parallelogram?

Step 1: Find x.

3x – 5 = 2x + 1

X – 5 = 1

X = 6

Step 2: Find y.

y = x + 2y = 6 + 2

y = 8

Page 6: 6-3 Proving that a Quadrilateral is a Parallelogram Objective: To determine whether a quadrilateral is a parallelogram Essential Understanding: You can.

and FINALLY

6-3 p. 372:7-15


7.3 Proving That a Quadrilateral Is a Parallelogram

7.3 Proving That a Quadrilateral Is a Parallelogram

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

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

8.3 show that a quadrilateral is a parallelogram

8.3 show that a quadrilateral is a parallelogram

endpoints AB - enderton.comenderton.com/umtymp/geomsheetfinal.pdf · A quadrilateral is a parallelogram if and only if both pairs of its opposite sides are parallel. A quadrilateral

endpoints AB - enderton.comenderton.com/umtymp/geomsheetfinal.pdf · A quadrilateral is a parallelogram if and only if both pairs of its opposite sides are parallel. A quadrilateral

Proving a Quadrilateral is a Parallelogram€¦ · Proving a Quadrilateral is a Parallelogram Thursday, January 31, 13 1. DeÞne converse ¥ What is the converse of this conditional?

Proving a Quadrilateral is a Parallelogram€¦ · Proving a Quadrilateral is a Parallelogram Thursday, January 31, 13 1. DeÞne converse ¥ What is the converse of this conditional?

4.5, 4.6 and 4.8 By Tamago and Faris. Today’s Special: QUADRILATERALS! Quadrilateral – a polygon with four sides o Parallelogram – a quadrilateral with.

4.5, 4.6 and 4.8 By Tamago and Faris. Today’s Special: QUADRILATERALS! Quadrilateral – a polygon with four sides o Parallelogram – a quadrilateral with.

 · 2016-11-27 · Check your answers by reading chapter 8 sections 1 , 2, ... Show that a Quadrilateral is a Parallelogram (8.3) ... Show that a Quadrilateral is a Parallelogram

 · 2016-11-27 · Check your answers by reading chapter 8 sections 1 , 2, ... Show that a Quadrilateral is a Parallelogram (8.3) ... Show that a Quadrilateral is a Parallelogram

Tests for Parallelograms. Objectives Recognize the conditions that ensure a quadrilateral is a parallelogram. Prove that a set of points forms a parallelogram.

Tests for Parallelograms. Objectives Recognize the conditions that ensure a quadrilateral is a parallelogram. Prove that a set of points forms a parallelogram.

Proving a Quadrilateral is a Parallelogram · 2015. 12. 14. · SWBAT: Prove a Quadrilateral is a Parallelogram quad has 2 sets of opp. sides || quad has 2 sets of opp. sides quad

Proving a Quadrilateral is a Parallelogram · 2015. 12. 14. · SWBAT: Prove a Quadrilateral is a Parallelogram quad has 2 sets of opp. sides || quad has 2 sets of opp. sides quad

6-3 Proving That a Quadrilateral Is a Parallelogram.

6-3 Proving That a Quadrilateral Is a Parallelogram.

8.3 Show that a Quadrilateral is a Parallelogrammrsluthismath.weebly.com/uploads/2/3/4/2/23420766/8.3.pdf · 522 Chapter 8 Quadrilaterals 8.3Show that a Quadrilateral is a Parallelogram

8.3 Show that a Quadrilateral is a Parallelogrammrsluthismath.weebly.com/uploads/2/3/4/2/23420766/8.3.pdf · 522 Chapter 8 Quadrilaterals 8.3Show that a Quadrilateral is a Parallelogram

Quadrilateral Proofs Packet #2 - White Plains Middle School · Quadrilateral Proofs – Packet #2 ... Properties of the Parallelogram *Parallelogram* 4 ... Day 2 - Ways to prove a

Quadrilateral Proofs Packet #2 - White Plains Middle School · Quadrilateral Proofs – Packet #2 ... Properties of the Parallelogram *Parallelogram* 4 ... Day 2 - Ways to prove a

Parallelograms have Properties Click to view What is a parallelogram? A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

Parallelograms have Properties Click to view What is a parallelogram? A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

mr-lee.weebly.com...If a quadrilateral is a parallelogram, then its opposite anqles are congruent. If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

mr-lee.weebly.com...If a quadrilateral is a parallelogram, then its opposite anqles are congruent. If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

5.9Show that a Quad. is a Parallel. Theorem 5.22 If both pairs of opposite ________ of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

5.9Show that a Quad. is a Parallel. Theorem 5.22 If both pairs of opposite ________ of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

How to Prove That a Quadrilateral is a Parallelogram With Everyone’s favorite parallelogram, Spongebob! Panos Tsaklas Paul Cheng Section 5.6 Mod. 7.

How to Prove That a Quadrilateral is a Parallelogram With Everyone’s favorite parallelogram, Spongebob! Panos Tsaklas Paul Cheng Section 5.6 Mod. 7.

6-1 The Polygon Angle-Sum Theorems 6-5 If a quadrilateral is a parallelogram, then its opposite angles are congruent. Theorem 6-6 If a quadrilateral is a parallelogram, ...

6-1 The Polygon Angle-Sum Theorems 6-5 If a quadrilateral is a parallelogram, then its opposite angles are congruent. Theorem 6-6 If a quadrilateral is a parallelogram, ...

theoremsaboutparallelogramstofindout: Parallelogram …...parallelogram, then its opposite sides are congruent. If a quadrilateral is a parallelogram, then its consecutive angles are

theoremsaboutparallelogramstofindout: Parallelogram …...parallelogram, then its opposite sides are congruent. If a quadrilateral is a parallelogram, then its consecutive angles are

6-5 Rhombi and Squares - Check Your Understandingphsmath.pbworks.com/f/Geom+6-5+Answers.pdfDetermine whether each quadrilateral is a parallelogram. Justify your answer. Quadrilateral

6-5 Rhombi and Squares - Check Your Understandingphsmath.pbworks.com/f/Geom+6-5+Answers.pdfDetermine whether each quadrilateral is a parallelogram. Justify your answer. Quadrilateral

Lesson 4 Menu 1.Determine whether the quadrilateral shown in the figure is a parallelogram. Justify your answer. 2.Determine whether the quadrilateral.

Lesson 4 Menu 1.Determine whether the quadrilateral shown in the figure is a parallelogram. Justify your answer. 2.Determine whether the quadrilateral.