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

Slides:

Advertisements

Similar presentations

Advertisements

8.3 Tests for Parallelograms

Are the opposite sides QU and AD congruent? (Use the distance formula!) NO, they aren’t congruent! (different lengths) Given quadrilateral QUAD Q(-3, 1)

6.5 Trapezoids and Kites Geometry Mrs. Spitz Spring 2005.

Trapezoids and Kites Geometry Unit 12, Day 5 Mr. Zampetti

Parallelograms and Tests for Parallelograms

Classifying Quadrilaterals

Warm Up Quiz 1. If the lengths of a right triangle are 5 and 10 what could the missing side be? [A] 75 [B] [C] 5 [D] If the hypotenuse of a

CLASSIFYING QUADRILATERALS DAY 2. Bellwork  Please begin working on P 293 (60-63)

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

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.

The Distance Formula Used to find the distance between two points: A( x1, y1) and B(x2, y2) You also could just plot the points and use the Pythagorean.

1. Given Triangle ABC with vertices A(0,0), B(4,8), and C(6,2).

Proof using distance, midpoint, and slope

Tests for Parallelograms Advanced Geometry Polygons Lesson 3.

Tests for Parallelograms

6. Show that consecutive angles are supplementary.

INTERIOR ANGLES THEOREM FOR QUADRILATERALS By: Katerina Palacios 10-1 T2 Geometry.

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.

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.

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.

Chapter 6: Quadrilaterals

Using Coordinate Geometry to Prove Parallelograms

6.3 Proving Quadrilaterals are 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.

Tests for Parallelograms

Chapter If opposite sides of a quadrilateral are //, then it is a //ogram. (definition) 2. If both pairs of opposite sides of a quadrilateral.

Homework: Quadrilaterals & Coordinate Geometry Day 1 Wkst

Proving Parallelograms: Coordinate Geometry Unit 1C3 Day 4.

Objectives: 1) To define and classify special types of quadrilaterals.

GEOMETRY HELP ABCD is a quadrilateral because it has four sides. Judging by appearance, classify ABCD in as many ways as possible. It is a trapezoid because.

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

Proving Properties of Triangles and Quadrilaterals

Review for Parallelogram Properties Quiz G.GPE.B.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that.

 Find x and  ABCD is a parallelogram and AB is twice BC. If the perimeter of the parallelogram is 24, find CD.

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.

Using the Distance Formula in Coordinate Geometry Proofs.

Quadrilaterals in the Coordinate Plane

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).

Lesson 7 Menu 1.In the figure, ABCD is an isosceles trapezoid with median EF. Find m  D if m  A = Find x if AD = 3x 2 – 5 and BC = x Find.

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

WARM-UP Worksheet in Packet YES, PARALLELOGRAM You MUST plot the quadrilateral for credit!!!

Aim: How can we solve coordinate quadrilateral proofs

EXAMPLE 4 Use coordinate geometry

Using Coordinate Geometry to Prove Parallelograms

Quadrilaterals and Coordinates Proof

Using Coordinate Geometry to Prove Parallelograms

6.3 Proving Quadrilaterals are Parallelograms

6.3 Proving Quadrilaterals are Parallelograms

6.3 Tests for Parallelograms

6.3 Proving Quadrilaterals are Parallelograms

6.3 Proving Quadrilaterals are Parallelograms

Day 108 – Rhombus and a parallelogram on x-y plane

9.2 Proving Quadrilaterals are Parallelograms

PROVING A QUADRILATERAL IS AN ISOSCELES TRAPEZOID

Quadrilaterals & Parallelograms

Quadrilaterals on the Coordinate Plane

6.3 Proving Quadrilaterals are Parallelograms

6.1: Classifying Quadrilaterals

6.6 Placing Figures in the coordinate plane

Proving a quadrilateral is a parallelogram

Proving a quadrilateral is a RHOMBUS

6.1: Classifying Quadrilaterals

Presentation transcript:

Coordinate Geometry Adapted from the Geometry Presentation by Mrs. Spitz Spring ads%20are%20Parallelograms.ppt

Using Coordinate Geometry When a figure is in the coordinate plane, you can use the Distance Formula to prove that sides are congruent and you can use the Slope Formula to prove sides are parallel or perpendicular. ads%20are%20Parallelograms.ppt

Ex: 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. ads%20are%20Parallelograms.ppt

Ex: Using properties of parallelograms Method 1—Show that opposite sides have the same slope, so they are parallel. Slope of AB.  3-(-1) = Slope of CD.  1 – 5 = – 6 Slope of BC.  5 – 3 = Slope of DA.  - 1 – 1 = AB and CD have the same slope, so they are parallel. Similarly, BC ║ DA. Because opposite sides are parallel, ABCD is a parallelogram. ads%20are%20Parallelograms.ppt

Ex: Using properties of parallelograms Method 2—Show that opposite sides have the same length. AB=√(1 – 2) 2 + [3 – (- 1) 2 ] = √17 CD=√(7 – 6) 2 + (1 - 5) 2 = √17 BC=√(6 – 1) 2 + (5 - 3) 2 = √29 DA= √(2 – 7) 2 + (-1 - 1) 2 = √29 AB ≅ CD and BC ≅ DA. Because both pairs of opposites sides are congruent, ABCD is a parallelogram. ads%20are%20Parallelograms.ppt

Ex: Using properties of parallelograms Method 3—Show that one pair of opposite sides is congruent and parallel. Slope of AB = Slope of CD = -4 AB=CD = √17 AB and CD are congruent and parallel, so ABCD is a parallelogram. ads%20are%20Parallelograms.ppt

Ex: Using properties of trapezoids Show that ABCD is a trapezoid. Compare the slopes of opposite sides.  The slope of AB = 5 – 0 = 5 = – 5 -5  The slope of CD = 4 – 7 = -3 = – 4 3 The slopes of AB and CD are equal, so AB ║ CD.  The slope of BC = 7 – 5 = 2 = 1 4 –  The slope of AD = 4 – 0 = 4 = 2 7 – 5 2 The slopes of BC and AD are not equal, so BC is not parallel to AD. So, because AB ║ CD and BC is not parallel to AD, ABCD is a trapezoid.

Homework Work Packet: Coordinate Geometry #1, 3, 4 Find all 4 slopes, all 4 distances, and name the figure