Aim: Slopes of Parallel Lines Course: Applied Geometry Do Now: a. y = 2x + 5 b. y = 2x – 1 c. y = 2x + 2 Aim: What is the relationship between slopes.

Slides:

Advertisements

Similar presentations

Advertisements

§ 2.4 The Slope of a Line.

Chapter 3.3 Slopes of Lines Check.3.1 Prove two lines are parallel, perpendicular, or oblique using coordinate geometry. Spi.3.1 Use algebra and coordinate.

4.7 Graphing Lines Using Slope Intercept Form

 An equation of a line can be written in slope- intercept form y = mx + b where m is the slope and b is the y- intercept.  The y-intercept is where.

Aim: Slope/Intercept Form of Equation Course: Applied Geometry Do Now: Graph the following equations on the same set of coordinate axes: Aim: What can.

Objectives: Define and explain the components of the slope-intercept form of a linear equation. Use the slope-intercept form of a linear equation. Standards.

Coordinates and Linear Equations Miss Hudson’s Maths.

Advanced Geometry. First you must prove or be given that the figure is a parallelogram, then A PARALLELOGRAM is a rectangle if… 1. It contains at least.

Michael Reyes MTED 301 Section 1-2. Subject: Geometry Grade Level:9-10 Lesson: The Distance Formula Objective: California Mathematics Content Standard.

Parallelograms and Tests for Parallelograms

3-3 Slopes of Lines You used the properties of parallel lines to determine congruent angles. Find slopes of lines. Use slope to identify parallel and perpendicular.

Classifying Quadrilaterals

Chin-Sung Lin. Mr. Chin-Sung Lin  Distance Formula  Midpoint Formula  Slope Formula  Parallel Lines  Perpendicular Lines.

Proof using distance, midpoint, and slope

Parallel and Perpendicular Lines Chap 4 Supplemental Lecture.

10. Undefined38. T; Alt Ext Angles T; Corr Angles 14. M = 150, average speed of 150 mi/h40. F; Same-Side Int Angles 16. neither 18. M = 1150/2400.

Sullivan Algebra and Trigonometry: Section 2.3 Objectives Calculate and Interpret the Slope of a Line Graph Lines Given a Point and the Slope Use the Point-Slope.

Slopes of Equations and Lines Honors Geometry Chapter 2 Nancy Powell, 2007.

Tests for Parallelograms

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.

What is the slope of the line that passes through (-2, 5) and (6, -10)? 15/8 8/15 -15/8 -8/15 [Default] [MC Any] [MC All]

Section 6.6 What we are Learning:

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

Using Coordinate Geometry to Prove Parallelograms

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

Notes Over 2.1 Graphing a Linear Equation Graph the equation.

Write equations of lines in point-slope form.

Homework: Quadrilaterals & Coordinate Geometry Day 1 Wkst

Proving Quadrilaterals on the Coordinate Plane February 27, 2013.

Warm up Recall the slope formula:

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.

Holt McDougal Algebra Slopes of Parallel and Perpendicular Lines Identify and graph parallel and perpendicular lines. Write equations to describe.

Proving Properties of Triangles and Quadrilaterals

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

Then: You recognized and applied properties of parallelograms. Now: Recognize the conditions that ensure a quadrilateral is a parallelogram. 6.3 TEST FOR.

3.5 Slope of a Line. What is Slope? Slope is a measure of the steepness of a line. When looking at a graph, we can determine slope by taking, or the vertical.

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

Geometry Unit 3rd Prep Ali Adel.

Aim: How can we solve coordinate quadrilateral proofs

Conditions for Special Parallelograms

Proving that a Quadrilateral Is a Parallelogram

EXAMPLE 4 Use coordinate geometry

Using Coordinate Geometry to Prove Parallelograms

Quadrilaterals in the Coordinate Plane

Linear Functions.

Chapter 3 Review Geometry.

Using Coordinate Geometry to Prove Parallelograms

Objective- To use slope and y-intercept to

Solving Problems Involving Lines and Points

WXYZ is a rectangle. If ZX = 6x – 4 and WY = 4x + 14, find ZX.

Day 7 – Parallel and Perpendicular lines

Coordinate Proofs Lesson 6-2.

6.3 Proving Quadrilaterals are Parallelograms

Warm up What is the equation of the line that goes through (1, 4) and (5, 12)? What is the distance between (1, 4) and (5, 12)? What is the equation of.

Classifying Quadrilaterals

concepts, and examples Lesson Objectives: I will be able to …

Are you ready for the test?

Day 109 – A trapezoid on the x-y plane

6-5: Conditions of Special Parallelograms

____ ? A. B. C. 5-Minute Check 1.

Warm up What is the equation of the line that goes through (1, 4) and (5, 12)? What is the distance between (1, 4) and (5, 12)? What is the equation of.

QUADRILATERAL TEST REVIEW

5.4 Finding Linear Equations

Functions Test Review.

Presentation transcript:

Aim: Slopes of Parallel Lines Course: Applied Geometry Do Now: a. y = 2x + 5 b. y = 2x – 1 c. y = 2x + 2 Aim: What is the relationship between slopes of parallel lines? What is the slope of each line? 2 2 2

Aim: Slopes of Parallel Lines Course: Applied Geometry Slopes of Parallel Lines Graph Equations a), b), and d) on the graphing calculator by 1.Clicking the Y = button and inputting Y1 = 2x + 5 Y2 = 2x – 1 Y3 = 2x Click the Graph key and watch the graphs appear. Hit the Trace key and skip from line to line. Lines having equal slopes are parallel. Lines having different slopes are not parallel.

Aim: Slopes of Parallel Lines Course: Applied Geometry Points A(-4, 2), B (1, 2), C(1, -3) and D(-4, -3) form a quadrilateral. a.Graph the points and draw quadrilateral ABCD b.What are the slopes of sides AB, BC, CD and AD? c.What kind of quadrilateral is ABCD? Explain Model Problem

Aim: Slopes of Parallel Lines Course: Applied Geometry Model Problem y B(1, 2) (-4, 2)A C(1, -3) (-4, -3)D 5 units 4 equal sides 4 right angles SQUARE Slope of AB = 0 Slope of CD = 0 Slope of AD = undefined Slope of BC = undefined Recall: Two lines are parallel if their slopes are equal and if the slopes of two lines are equal, the lines are parallel. AB || CD & AD || BC

Aim: Slopes of Parallel Lines Course: Applied Geometry Model Problem Quadrilateral ABCD has vertices A(0,-1), B(0,1), C(3,4), and D(3,2). Using coordinate geometry, determine what type of quadrilateral ABCD is. A B C(3,4) (0,1) (0,-1) (3,2)D Just showing the graph is not enough - prove using the formula for slope. Since the slope of BC and AD are the same, the lines are parallel. Since the slope of AB and CD are the same, the lines are parallel. BC || AD, AB || CD, ABCD is a parallelogram.

Aim: Slopes of Parallel Lines Course: Applied Geometry Model Problem Graph a line that is parallel to the line y = 2x – 2 and that has a y-intercept of 4 What is the equation of this new line? (0, 4) (1, 6) (0, -2) y = 2x - 2 y = 2x + 4 m = 2 b = 4 y = mx + b b = -2

Aim: Slopes of Parallel Lines Course: Applied Geometry Model Problem Graph a line that is parallel to the line y = 1/2x – 4 and that passes through point (2, 2) What is the equation of this new line? m = 1/2 y = 1/2x – 4 y = 1/2x + 1 y = mx + b m = 1/2b = 1 (4, 3) (2, 2) (0, -4) b = -4 (0, 1)

Aim: Slopes of Parallel Lines Course: Applied Geometry On Sketchpad: Graph a line that is parallel to the line y = -1/4x + 3 and that passes through (3, 0). Sketchpad: Graph  Plot New Function  y = -1/4x + 3  Enter Graph  Plot Points  (3, 0)  Plot Plot a second point that would result in a line parallel to y = -1/4x + 3 Highlight new line  Measure  Slope and a 2 nd time for Equation. On your calculator, sent the new equation Y 1 = Model Problem

Aim: Slopes of Parallel Lines Course: Applied Geometry Model Problem Graph a line that is parallel to the line y = 2x + 1 and that passes through (0, -2).

Aim: Slopes of Parallel Lines Course: Applied Geometry Model Problem Graph a line that is parallel to the line y = -4x – 5 and that passes through (0, 2).

Aim: Slopes of Parallel Lines Course: Applied Geometry Model Problem Graph a line that is parallel to the line y = -4 and that passes through (0, -6).

Aim: Slopes of Parallel Lines Course: Applied Geometry Model Problem Graph a line that is parallel to the line y = 1/3x – 6 and that passes through (1, 2).

Aim: Slopes of Parallel Lines Course: Applied Geometry Model Problem Graph a line that is parallel to the line 2y = 4x – 6 and that passes through (-2, -4).