6.3 Proving that a Quadrilateral is a Parallelogram

Slides:

Advertisements

Similar presentations

Objectives State the conditions under which you can prove a quadrilateral is a parallelogram.

Advertisements

6-2 Properties of Parallelograms

Created by chris markstrum © Proving Quadrilaterals are Parallelograms California State Standards for Geometry 4: Prove basic theorems involving.

Proving Quadrilaterals are Parallelograms Lesson 6.3 Chapter 6 Section 6.3 Proving Quadrilaterals Are Parallelograms.

Objective: Prove that a given quadrilateral is a parallelogram. 6.3 Proving Quadrilaterals are Parallelograms Handbook, p. 19.

Proving that a Quadrilateral is a Parallelogram

6-3 Proving That a Quadrilateral Is a Parallelogram

Created by chris markstrum © Proving Quadrilaterals are Parallelograms Objective: To learn how to prove quadrilaterals are parallelograms.

Proving that a quadrilateral is a Parallelogram Geometry Regular Program SY Source: Discovering Geometry (2008) by Michael Serra Geometry (2007)

Warm Up: Day 2 Find the coordinates of point M in parallelogram PRAM.

Proving Quadrilaterals are Parallelograms - Sec 6.3 GOALS: To prove a quadrilateral is a parallelogram (6 ways to do so!)

OBJECTIVE: PROVING THAT A QUADRILATERAL IS A PARALLELOGRAM

8.6 Examples Example 1 STUV has at least one pair of consecutive sides that are congruent. What type of quadrilateral meets this condition? (rhombus,

Showing quadrilaterals are parallelograms. Bell Ringer.

A Study of all things 4 sided. Quadrilaterals Parallelograms.

Parallelograms Unit 8.2. What is a parallelogram Definition: a parallelogram is a quadrilateral with both pairs of opposite sides parallel.

Tests for Parallelograms

6. Show that consecutive angles are supplementary.

Polygons – Parallelograms A polygon with four sides is called a quadrilateral. A special type of quadrilateral is called a parallelogram.

EXAMPLE 4 Use coordinate geometry SOLUTION One way is to show that a pair of sides are congruent and parallel. Then apply Theorem 8.9. First use the Distance.

6.3 Proving Quadrilaterals are Parallelograms Day 3.

What is a quadrilateral? List as many types of quadrilaterals that you can think of.

6.3 Showing Quadrilaterals are Parallelograms Textbook pg 316.

Ways of proving a quadrilaterals are parallelograms Section 5-2.

Chapter 8.2 Notes: Use Properties of Parallelograms

EXAMPLE 3 List properties of special parallelograms

Ways to Prove that Quadrilaterals are Parallelograms

Conditions for Parallelograms Students will be able to show that a given quadrilateral is a parallelogram.

Geometry 6.3 I can recognize the conditions that ensure a quadrilateral is a parallelogram.

6.3 Proving Quadrilaterals are Parallelograms. Theorem If both pairs of opposite sides of a quadrilateral are parallel, then it is a parallelogram.

Properties of Parallelograms Definition  Parallelogram – a quadrilateral with both pairs of opposite sides parallel.

7.2 Parallelograms. Definition: A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Consecutive angles Opposite angles.

6-2 Properties of Parallelograms. Quadrilaterals In a quadrilateral, opposite sides do not share a vertex and opposite angles do not share a side. – In.

Parallelograms Properties & Attributes. Parallelograms …are quadrilaterals in which both pairs of opposite sides are parallel If a quadrilateral is a.

Lesson: Objectives: 6.5 Squares & Rhombi  To Identify the PROPERTIES of SQUARES and RHOMBI  To use the Squares and Rhombi Properties to SOLVE Problems.

8.2 – Use Properties of Parallelograms Goal: You will find angle and side measures in parallelograms.

Proving Quadrilaterals are Parallelograms Section 6.3 November 16, 2001.

 6.3 Showing Quadrilaterals are Parallelograms. We can use the theorems from 6.2 to prove that quadrilaterals are parallelograms  What 5 facts are ALWAYS.

Geometry Lesson 6 – 2 Parallelograms Objective: Recognize and apply properties of the sides of angles of parallelograms. Recognize and apply properties.

Interior and exterior angles. Exterior and interior angles are supplementary.

Sections  A parallelogram must have:  Both pair of opposite sides congruent  Both pair of opposite angles congruent  Consecutive angles that.

Warm-Up ABCD is a parallelogram. AB = 12 and BC = 25

6-3 Proving a Quad is a parallelogram

Properties of Parallelograms

8.2 Parallelograms.

EXAMPLE 4 Use coordinate geometry

Warm Up 6.3 on desk Do daily Quiz 6.2.

: Parallelograms Objectives:

Parallelograms.

Chapter 5 -- Quadrilaterals

Ways to Prove Quadrilaterals are Parallelograms

Polygons – Parallelograms

Parallelograms Parallelogram - A quadrilateral with both pairs of opposite sides parallel. Theorem 8.3 Opposite sides of a parallelogram are congruent.

Lecture 6-4 Rhombi and Squares.

6-2 Properties of Parallelograms

Section 5-1 Parallelograms.

Six Properties of Parallelograms

Bellringer Have your Homework (p. 356 #7-11, p. 364 #9-27 skip #13) and Notes out on your Desk Work on p. 363 #1 – 5.

Unit 6 Quadrilaterals Section 6.1 Properties of Parallelograms

Lesson 61 Determining if a Quadrilateral is a Parallelogram

6.3 Proving Quadrilaterals are Parallelograms

6-1 Parallelograms Objectives:

6.2 and 6.3: Quadrilaterals and Parallelograms

6.3 Conditions for Parallelograms

Proving Quadrilaterals Are Parallelograms

Properties of Parallelograms

6.3 Proving Quadrilaterals and Parallelograms

6 – 3 Proving That a Quadrilateral Is a Parallelogram

Bellringer Can a triangle have the sides with the given lengths? Explain 8mm, 6mm, 3mm 5ft, 20ft, 7ft 3m, 5m, 8m.

Presentation transcript:

6.3 Proving that a Quadrilateral is a Parallelogram If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Theorem 6.9 If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.

Theorem 6.10 If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Finding Values for Parallelograms For what value of y must PQRS be a parallelogram? 3x – 5 = 2x + 1 x – 5 = 1 x = 6 y = x + 2 y = 6 + 2 y = 8

Theorem 6.11 If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Theorem 6.12 If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.

Deciding Whether a Quadrilateral is a Parallelogram Can you prove that the quadrilateral is a parallelogram based on the diagram? Explain. No. You need to show that both pairs of opposite sides are congruent, not consecutive sides. Yes, same-side interior angles are supplementary, making segment AB and segment DC parallel. Since segment AB is congruent to segment DC, ABCD is a parallelogram.

Concept Summary Proving that a Quadrilateral is a Parallelogram

More Practice!!!!! Homework – Textbook p. 372 #7 – 16 ALL.