Finding Distance by using the Pythagorean Theorem

Slides:

Advertisements

Similar presentations

Proving the Distance Formula

Advertisements

Measurement Pythagorean Relationship 3 (Finding the length of an unknown leg)

The Pythagorean Theorem Presented by: Tanya Van Dam Kalles Junior High Algebra 2 Spring 2000.

Locating Points & Finding Distances

Introduction It is not uncommon for people to think of geometric figures, such as triangles and quadrilaterals, to be separate from algebra; however, we.

Lesson 7-2 Lesson 7-2: The Pythagorean Theorem1 The Pythagorean Theorem.

Distances in Coordinate Geometry

The Distance Formula Finding The Distance Between Points On maps and other grids, you often need to find the distance between two points not on the same.

Using the Pythagorean Theorem in 3-Dimensional Shapes.

Pythagorean Triples In addition to level 3.0 and beyond what was taught in class, the student may:  Make connection with other concepts in math.

The Pythagorean Theorem. The Right Triangle A right triangle is a triangle that contains one right angle. A right angle is 90 o Right Angle.

The Pythagorean Theorem x z y. For this proof we must draw ANY right Triangle: Label the Legs “a” and “b” and the hypotenuse “c” a b c.

The Pythagorean Theorem Objective: Find the length of a using the Pythagorean Theorem.

Lesson 10.1 The Pythagorean Theorem. The side opposite the right angle is called the hypotenuse. The other two sides are called legs. We use ‘a’ and ‘b’

4.4: THE PYTHAGOREAN THEOREM AND DISTANCE FORMULA

Geometry 1-6 Midpoint and Distance. Vocabulary Coordinate Plane- a plane divided into four regions by a horizontal line (x-axis) and a vertical line (y-axis).

8-1, 1-8 Pythagorean Theorem, Distance Formula, Midpoint Formula

Benchmark 40 I can find the missing side of a right triangle using the Pythagorean Theorem.

Pythagorean Theorem Use the Pythagorean Theorem to find the missing length of the right triangle. 1.

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.

Pythagorean Theorem Unit 7 Part 1. The Pythagorean Theorem The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.

How do we determine absolute value of complex numbers? Do Now: Explain “absolute value.” What is the distance formula? Do Now: Explain “absolute value.”

11.4 Pythagorean Theorem Definitions Pythagorean Theorem

4.4 Pythagorean Theorem and the Distance Formula Textbook pg 192.

1.9 Distance & Midpoint Formulas Circles Objectives –Find the distance between two points. –Find the midpoint of a line segment. –Write the standard form.

The Pythagorean Theorem Use the Pythagorean Theorem to find the missing measure in a right triangle including those from contextual situations.

Pythagorean Theorem & its Converse 8 th Grade Math Standards M.8.G.6- Explain a proof of the Pythagorean Theorem and its converse. M.8.G.7 - Apply the.

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.

10-1 The Pythagorean Theorem. LEGS Hypotenuse Problem 1: Finding the Length of a Hypotenuse The tiles shown below are squares with 6-in. sides. What.

Midpoint and distance formulas

Using the Pythagorean Theorem in 3-Dimensional Shapes

Pythagorean Theorem and it’s Converse

Pythagorean theorem.

The Distance and Midpoint Formulas

Midpoint and Distance in the Coordinate Plane

Right Triangle The sides that form the right angle are called the legs. The side opposite the right angle is called the hypotenuse.

Practice, Practice, Practice!

Lesson 4.7 Objective: To learn how to prove triangles are congruent and general statements using Coordinate Proofs.

Midpoint And Distance in the Coordinate Plane

Section 1.1 – Interval Notation

Distance on the Coordinate Plane

Introduction It is not uncommon for people to think of geometric figures, such as triangles and quadrilaterals, to be separate from algebra; however, we.

Pythagorean Theorem and Distance

1-6 Midpoint & Distance in the Coordinate Plane

Notes Over Pythagorean Theorem

Objectives Develop and apply the formula for midpoint.

PYTHAGOREAN THEOREM VOCABULARY.

P.5 The Cartesian Plane Our goals are to learn

6-3 The Pythagorean Theorem Pythagorean Theorem.

5-7 The Pythagorean Theorem

Chapter 1: Lesson 1.1 Rectangular Coordinates

Math Humor Q: What keeps a square from moving?.

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

In the diagram at the left, AB is a horizontal line segment.

7.0: Pythagorean Theorem Objectives:

The Pythagorean Theorem

Unit 5: Geometric and Algebraic Connections

Finding Distance by using the Pythagorean Theorem

In the diagram at the left, AB is a horizontal line segment.

Pythagoras' Theorem.

PYTHAGOREAN THEOREM VOCABULARY.

Midpoints and Distance

Pythagorean Theorem, its Converse and the coordinate system

1.7 Midpoint and Distance in the Coordinate Plane

Using Coordinates to Prove Geometric Theorems with Slope and Distance

The Pythagorean Theorem

10-1 The Pythagorean Theorem

Triangle Relationships

1-6: Midpoint and Distance

Presentation transcript:

Finding Distance by using the Pythagorean Theorem

Focus 5 - Learning Goal #1: Students will understand and apply the Pythagorean Theorem. 4 3 2 1 In addition to level 3.0 and beyond what was taught in class, the student may: Make connection with other concepts in math. Make connection with other content areas. Explain the relationship between the Pythagorean Theorem and the distance formula. The student will understand and apply the Pythagorean Theorem. Prove the Pythagorean Theorem and its converse. Apply the Pythagorean Theorem to real world and mathematical situations. Find the distance between 2 points on a coordinate plane using the Pythagorean Theorem. The student will understand the relationship between the areas of the squares of the legs and area of the square of the hypotenuse of a right triangle. Explain the Pythagorean Theorem and its converse. Create a right triangle on a coordinate plane, given 2 points. With help from the teacher, the student has partial success with level 2 and level 3 elements. Plot 3 ordered pairs to make a right triangle Identify the legs and the hypotenuse of a right triangle Find the distance between 2 points on the coordinate grid (horizontal and vertical axis). Even with help, students have no success with the unit content.

What is the Pythagorean Theorem?

What is the distance between (-2, 1) and (1, 5)? Draw a line connecting the points. Draw in lines that would make a right angled triangle, using these two points as corners.

What is the distance between (-2, 1) and (1, 5)? Find the length of the horizontal side. (subtract the x’s = 1 – -2) 3 Find the length of the vertical side. (subtract the y’s = 5-1) 4 4 3

What is the distance between (-2, 1) and (1, 5)? Use the Pythagorean Theorem to find the missing side. a2 + b2 = c2 32 + 42 = c2 9 + 16 = c2 25 = c2 c 4 3

What is the distance between (-6, 6) and (1, -4)? Draw in the line to connect the dots. Draw in the horizontal and vertical lines. Find the lengths of the horizontal and vertical lines. Horizontal 1 - -6 Vertical -4 - 6 10 c 7

What is the distance between (-6, 6) and (1, -4)? Use the Pythagorean Theorem to find the missing side. a2 + b2 = c2 102 + 72 = c2 100 + 49 = c2 149 = c2 10 c 7 𝟏𝟒𝟗 Is between 12 and 13.