Bell Ringer 2. 3. 1..

Slides:



Advertisements
Similar presentations
6.3 Proving that a Quadrilateral is a Parallelogram
Advertisements

6-2 Properties of 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
Bell Ringer.
Use Properties of Parallelograms
6.2 Properties of Parallelograms
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.
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!)
Showing quadrilaterals are parallelograms. Bell Ringer.
A Study of all things 4 sided. Quadrilaterals Parallelograms.
6.1 POLYGONS. VOCABULARY Polygon: plane figure formed by three or more segments (called sides). Diagonal: segment that joins 2 non- consecutive vertices.
Parallelograms Unit 8.2. What is a parallelogram Definition: a parallelogram is a quadrilateral with both pairs of opposite sides parallel.
Tests for Parallelograms
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.
6.3 Proving Quadrilaterals are Parallelograms Learning Target I can use prove that a quadrilateral is a parallelogram.
Goal: Identify special quadrilaterals
Ways of proving a quadrilaterals are parallelograms Section 5-2.
Chapter 8.2 Notes: Use Properties of Parallelograms
6-4 Properties of Rhombuses, Rectangles, and Squares
EXAMPLE 3 List properties of special parallelograms
Use Properties of Parallelograms
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.
Date: Topic: Properties of Parallelograms (7.1) Warm-up Find x and the missing angle measures The angles of a triangle add up to 180 degrees. 3x + 4x +
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.
6.2 Parallelograms Objectives Recognize and apply properties of the sides and angles of parallelograms. Recognize and apply properties of the diagonals.
8.2 Properties of Parallelograms
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.
Properties of Parallelograms Warm Up 3/17  Find the perimeter of triangle ABC: B 4 cm 3 cm 6 cm 2x cm x + 4 cm 4 cm A C.
Warm-Up ABCD is a parallelogram. AB = 12 and BC = 25
1. Find the value of x. ANSWER 60 2.
6.4 EQ: What properties do we use to identify special types of parallelograms?
Unit 9 Lesson 6.2A: Parallelograms
Properties of Parallelograms
6.2 Properties of Parallelograms
8.2 Parallelograms.
EXAMPLE 4 Use coordinate geometry
Parallelograms.
6-2B Proving Quadrilaterals Are 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.
Properties of Parallelograms
6-2 Properties of Parallelograms
Section 5-1 Parallelograms.
7.1 Properties of Parallelograms
Six Properties of Parallelograms
Properties of Parallelograms
Bell Ringer: What do you know about quadrilaterals and parallelograms?
8.2 Use Properties of Parallelograms
6.2 Properties of Parallelograms
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
Module 15: Lesson 6 Properties of Parallelograms
6.3 Conditions for Parallelograms
Proving Quadrilaterals Are Parallelograms
Properties of Parallelograms
6.3 Proving Quadrilaterals and Parallelograms
Presentation transcript:

Bell Ringer 2. 3. 1.

Properties of Parallelograms

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

Find Side Lengths of Parallelograms Example 1 Find Side Lengths of Parallelograms FGHJ is a parallelogram. Find JH and FJ. SOLUTION JH = FG Opposite sides of a are congruent. Substitute 5 for FG. = 5 FJ = GH Opposite sides of a are congruent. Substitute 3 for GH. = 3 ANSWER In FGHJ, JH = 5 and FJ = 3. 4

Now You Try  Find Side Lengths of Parallelograms ABCD is a parallelogram. Find AB and AD. 1. ANSWER AB = 9; AD = 8

Find Angle Measures of Parallelograms Example 2 Find Angle Measures of Parallelograms PQRS is a parallelogram. Find the missing angle measures. SOLUTION By Theorem 6.3, the opposite angles of a parallelogram are congruent, so mR = mP = 70°. 1. 2. By Theorem 6.4, the consecutive angles of a parallelogram are supplementary. Consecutive angles of a are supplementary. mQ + mP = 180° Substitute 70° for mP. mQ + 70° = 180° Subtract 70° from each side. mQ = 110° 6

Example 2 Find Angle Measures of Parallelograms By Theorem 6.3, the opposite angles of a parallelogram are congruent, so mS = mQ = 110°. 3. ANSWER The measure of R is 70°, the measure of Q is 110°, and the measure of S is 110°. 7

Now You Try  mB = 120° mC = 60° mD = 120° ANSWER mA = 75° Find Angle Measures of Parallelograms ABCD is a parallelogram. Find the missing angle measures. 2. ANSWER mB = 120° mC = 60° mD = 120° ANSWER mA = 75° mB = 105° mC = 75° 3.

Find Segment Lengths Diagonals of a bisect each other. Example 3 Find Segment Lengths TUVW is a parallelogram. Find TX. SOLUTION TX = XV Diagonals of a bisect each other. Substitute 3 for XV. = 3 9

Now You Try 

Now You Try 

Now You Try 

Now You Try 

Now You Try 

Now You Try 

Page 313

Complete Page 313 #s 14-36 even only