Proving Parallelograms: Coordinate Geometry Unit 1C3 Day 4.

Slides:

Advertisements

Similar presentations

8.3 Tests for Parallelograms

Advertisements

CP Geometry Mr. Gallo. Classifying Polygons in the Coordinate Use three formulas: FormulaWhen to Use it Distance FormulaTo determine whether: Sides are.

Parallelograms and Tests for Parallelograms

TODAY IN GEOMETRY…  REVIEW: Properties of Parallelograms  Practice QUIZ  Learning Target : 8.3 Prove a quadrilateral is a parallelogram  Independent.

6-3 Proving That a Quadrilateral Is a Parallelogram

The Conic Sections Chapter 10. Introduction to Conic Sections (10.1) 4 A conic section is the intersection of a plane with a double-napped cone.

COORDINATE GEOMETRY PROOFS USE OF FORMULAS TO PROVE STATEMENTS ARE TRUE/NOT TRUE: Distance: d= Midpoint: midpoint= ( ) Slope: m =

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

Quadrilaterals in the Coordinate Plane I can find the slope and distance between two points I can use the properties of quadrilaterals to prove that a.

Rectangle Proofs A rectangle is a parallelogram with four right angles and congruent diagonals.

Proof using distance, midpoint, and slope

Tests for Parallelograms Advanced Geometry Polygons Lesson 3.

6.7 Polygons in the Coordinate Plane

Tests for Parallelograms

©thevisualclassroom.com 2.11 Verifying Geometric Properties When proving sides of a quadrilateral are parallel use slope When proving sides are perpendicular,

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.

Polygons In The Coordinate Plane Chapter 6 Section 7.

Polygons in the Coordinate Plane Techniques Examples Practice Problems.

Coordinate Geometry Adapted from the Geometry Presentation by Mrs. Spitz Spring 2005

Using Coordinate Geometry to Prove Parallelograms

UNIT 7 LESSON 4B PROVING PARALLELOGRAMS CCSS G-CO 11: Prove theorems about parallelograms. LESSON GOALS Use properties of parallelograms to prove that.

6.3 TESTS FOR PARALLELOGRAMS. If… Both pairs of opposite sides are parallel Both pairs of opposite sides are congruent Both pairs of opposite angles are.

6-3 Tests for Parallelograms You recognized and applied properties of parallelograms. Recognize the conditions that ensure a quadrilateral is a parallelogram.

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

Geometry 6-4 Properties of Rhombuses, Rectangles, and Squares.

Proofs with Quadrilaterals. Proving Quadrilaterals are Parallelograms Show that opposite sides are parallel by same slope. Show that both pairs of opposite.

7.2/7.3 Parallelograms! Learning Objective: to identify and classify parallelograms and prove that figures are special types of parallelograms. Warm-up.

6.3 Proving Quadrilaterals are Parallelograms. Objectives: Prove that a quadrilateral is a parallelogram. Use coordinate geometry with parallelograms.

Pre-Requisite Information Pre-Calculus Day 1. Standard Form Ax + By= C NO FRACTIONS A cannot be negative Slope is –A/B Parallel Lines Perpendicular Lines.

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

Geometry Section 6.3 Conditions for Special Quadrilaterals.

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

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

Do-Now Solve the following proportions. Is it possible to prove the lines parallel? If so, state a reason. 82° 98° 100° Main.

8.3 Test for Parallelograms Check.3.2 Connect coordinate geometry to geometric figures in the plane (e.g. midpoints, distance formula, slope, and polygons).

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.

G-05 “I can use coordinates to prove and apply properties of parallelograms.” Parallelogram, rectangle, rhombus and squares.

Aim: How can we solve coordinate quadrilateral proofs

Math 3 Unit 3 Lesson: 2 Parallelograms

Parallelogram, rectangle, rhombus and squares

Continuation of MVP 8.3 PROVE IT!

Coordinate Geometry Notes Name:____________________________

EXAMPLE 4 Use coordinate geometry

Using Coordinate Geometry to Prove Parallelograms

Lesson 8.3: Show that a Quadrilateral is a Parallelogram

Quadrilaterals and Coordinates Proof

Quadrilaterals and Coordinates Proof

Parallelograms.

Section 6.6 Polygons in the Coordinate Plane

Ways to Prove Quadrilaterals are Parallelograms

Using Coordinate Geometry to Prove Parallelograms

Lesson: 6.3 Tests for Parallelograms Objectives:

6-3: Tests for Parallelograms

CONDITIONS FOR PARALLELOGRAM

6-3 Conditions for ||’ograms

6-3 Tests for Parallelograms

Lesson 61 Determining if a Quadrilateral is a Parallelogram

PROVING A QUADRILATERAL IS AN ISOSCELES TRAPEZOID

6.3 Proving Quadrilaterals are Parallelograms

6.6 Placing Figures in the coordinate plane

Proving a quadrilateral is a parallelogram

Proving a quadrilateral is a RHOMBUS

Properties of Parallelograms

6.3 Proving Quadrilaterals and Parallelograms

BELLWORK Find the midpoint between the following pairs of points.

Presentation transcript:

Proving Parallelograms: Coordinate Geometry Unit 1C3 Day 4

Do Now For two points in a coordinate plane, (x 1, y 1 ) and (x 2, y 2 )…  What is the distance formula?  What is the slope formula?  What is the midpoint formula?

Using Coordinate Geometry  When a figure is in the coordinate plane, you can use the ________________________ to prove that sides are congruent.  You can use the _____________________ to prove sides are parallel.

Ex. 1: Using properties of parallelograms  Show that A(2, -1), B(1, 3), C(6, 5) and D(7,1) are the vertices of a parallelogram.

Ex. 1a: Using properties of parallelograms  Method 1—Show that opposite sides have the same slope, so they are parallel.

Ex. 1b: Using properties of parallelograms  Method 2—Show that opposite sides have the same length.

Ex. 1c: Using properties of parallelograms  Method 3—Show that one pair of opposite sides is congruent and parallel.

Ex. 1d: Using properties of parallelograms  Method d— Show that diagonals bisect each other.

Ex. 2: Proving Parallelograms

Closure  Could a hexagon with opposite sides parallel be called a parallelogram? Explain.