Lesson 1-2 Section 1-4. Postulate Definition Example 1.

Slides:



Advertisements
Similar presentations
Combinations of Functions
Advertisements

The Distance Formula Understand horizontal/vertical distance in a coordinate system as absolute value of the difference between coordinates; develop.
The Distance Formula & Equations of Circles
Lesson 7-2 Lesson 7-2: The Pythagorean Theorem1 The Pythagorean Theorem.
1-7: Midpoint and Distance in the Coordinate Plane
4.4: THE PYTHAGOREAN THEOREM AND DISTANCE FORMULA
Distance and Midpoints
Index Card Let’s start our stack of Theorems, Postulates, Formulas, and Properties that you will be able to bring into a quiz or test. Whenever I want.
Lesson 1-3 Section 1-5. Definition  To find the Midpoint of a number line, we simply take the average of the distance.  Say that we are trying to find.
1.3 Distance and Midpoints
Midpoint and Distance Formulas Section 1.3. Definition O The midpoint of a segment is the point that divides the segment into two congruent segments.
Chapter 1, Section 6. Finding the Coordinates of a Midpoint  Midpoint Formula: M( (x1+x2)/2, (y1+y2)/2 )  Endpoints (-3,-2) and (3,4)
Section 11.6 Pythagorean Theorem. Pythagorean Theorem: In any right triangle, the square of the length of the hypotenuse equals the sum of the squares.
Basics. Undefined terms Point: a dot, no dimension Line: a line the an arrow on each end, one dimension Plane: two dimensions.
3.6 Perpendiculars and Distance
Section 1-3 Segments, Rays, and Distance. line; segment; ray;
TOOLS OF GEOMETRY UNIT 1. POINTS, LINES, AND PLANES Essential Understanding: Geometry is a mathematical system built on accepted facts, basic terms, and.
Lesson 3-3 Section 3-4. Remember Postulate Example 1.
Intro to Polar Coordinates Lesson 6.5A. 2 Points on a Plane  Rectangular coordinate system Represent a point by two distances from the origin Horizontal.
Polar Coordinates Lesson Points on a Plane Rectangular coordinate system  Represent a point by two distances from the origin  Horizontal dist,
Applying the Pythagorean Theorem and Its Converse Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson.
1.7: Midpoint and Distance in the Coordinate Plane Part II.
TOOLS OF GEOMETRY UNIT 1. TOOLS OF GEOMETRY Date Essential Question How is the Pythagorean Theorem used to find the distance between two points? Home.
Pre-Calculus Coordinate System. Formulas  Copy the following formulas into your notes. –Distance Formula for Coordinate Plane –Midpoint Formula for Coordinate.
Postulate: A rule that is accepted without proof (also called an axiom). The first point A A x1x1 The second point B B x2x2 How do you find the distance.
1.3 Segments and Measure The segment postulate Distance Formula.
Pythagorean Theorem & Distance Formula Anatomy of a right triangle The hypotenuse of a right triangle is the longest side. It is opposite the right angle.
Distance on a coordinate plane. a b c e f g d h Alternate Interior angles Alternate exterior angles corresponding angles supplementary angles.
Mr. Kelley/Mr. Riddell GEOMETRY B WELCOME! 1.Syllabus 2.Questions? 3.Let’s get to work!
Do Now – Geometry Take your seats and solve the following problem Use the figure to answer the questions. a) The flat surfaces of the pyramid are called.
Applying the Pythagorean Theorem and Its Converse 3-9 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson.
Midpoint And Distance in the Coordinate Plane
1-7: Midpoint and Distance in the Coordinate Plane
Warm-up 7-8.
Lesson 4.7 Objective: To learn how to prove triangles are congruent and general statements using Coordinate Proofs.
Distance and Midpoints
Midpoint And Distance in the Coordinate Plane
Measuring and Constructing Line Segments
Lesson 3-6: Perpendicular & Distance
1-6 Midpoint and Distance in the Coordinate Plane Warm Up
Objectives Develop and apply the formula for midpoint.
8.3 Polar Form of Complex Numbers
Section 1.1 – Interval Notation
Unit 1 Review.
Distance on the Coordinate Plane
1.3 Segments & Their Measures
Lesson: 10 – 8 Equations of Circles
Objectives Develop and apply the formula for midpoint.
Chapter 1: Tools of Geometry
Notes #3 (1.3) 1-3 Distance and Midpoints
The sum of any two even integers is even.
Chapter 1: Lesson 1.1 Rectangular Coordinates
5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA
Lesson 8.11 Finding Distances on the Coordinate Plane
1-6 Midpoint and Distance in the Coordinate Plane Warm Up
1.7 Midpoint and Distance in the Coordinate Plane
The Distance Formula     Understand horizontal/vertical distance in a coordinate system as absolute value of the difference between coordinates;
The Pythagorean Theorem
Distance between two points
Unit 3: Coordinate Geometry
Chapter 9 Section 8: Equations of Circles.
Measuring Segments Chapter 1.4.
Objectives Develop and apply the formula for midpoint.
Using Properties of Parallel Lines
Use Segments and Congruence & Midpoints
1-6 Midpoint and Distance in the Coordinate Plane Warm Up
1.7 Midpoint and Distance in the Coordinate Plane
1-6 Midpoint and Distance in the Coordinate Plane Warm Up
1.3 Segments & Their Measures
The Distance Formula     Understand horizontal/vertical distance in a coordinate system as absolute value of the difference between coordinates;
Presentation transcript:

Lesson 1-2 Section 1-4

Postulate

Definition

Example 1

Example 2

Definition

Construction

Postulate

Example 3

Example 4

Example 5

What about the distance?  We used the ruler postulate for finding the distance between two points on a line, but how can we find the distance of a line in a coordinate plane?  Let’s see…..

Definition

Example 6

Example 7

Is there another way?  We have now mastered finding the distance between two points in the coordinate plane. However, there is another way of going about it.  We can use a very famous theorem: The Pythagorean Theorem. Let’s see how we do that….

Definition

Example 8

Example 8 cont.

Example 9

Practice  Try the following problems:  Pg. 32 # 5-15 odd, 12