8-1 Vocabulary Geometric mean.

Slides:

Advertisements

Similar presentations

8-1 Similarity in Right Triangles

Advertisements

Similarity in Right Triangles

Similarity in Right Triangles

Lesson 8 – 1 Geometric Mean

Geometric Mean Theorem I

8-1 Similarity in Right Triangles

Altitudes Recall that an altitude is a segment drawn from a vertex that is perpendicular to the opposite of a triangle. Every triangle has three altitudes.

Objectives Use geometric mean to find segment lengths in right triangles. Apply similarity relationships in right triangles to solve problems.

8-1 Similarity in right triangles

Similarity in Right Triangles Students will be able to find segment lengths in right triangles, and to apply similarity relationships in right triangles.

APPLYING RIGHT TRIANGLES AND TRIGONOMETRY. OBJECTIVE: SWBAT… FIND THE GEOMETRIC MEAN BETWEEN 2 NUMBERS SOLVE PROBLEMS INVOLVING RELATIONSHIPS BETWEEN.

Objectives Use geometric mean to find segment lengths in right triangles. Apply similarity relationships in right triangles to solve problems.

7.4 Similarity in Right Triangles

9.1 Similar Right Triangles

Section 7.4 Similarity in Right Triangles. Geometric Mean The positive number of x such that ═

7.4 Similarity in Right Triangles In this lesson we will learn the relationship between different parts of a right triangle that has an altitude drawn.

Section 8-1 Similarity in Right Triangles. Geometric Mean If a, b, and x are positive numbers and Then x is the geometric mean. x and x are the means.

Geometry 8.1 Right Triangles.

7.4 Similarity in Right Triangles

Similarity in Right Triangles

Holt Geometry 8-1 Similarity in Right Triangles Warm Up 1. Write a similarity statement comparing the two triangles. Simplify Solve each equation.

GEOMETRY 10-3 Similarity in Right Triangles Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Warm Up Week 7. Section 9.1 Day 1 I will solve problems involving similar right triangles. Right Triangle – Altitude to Hypotenuse If the altitude.

Holt Geometry 8-1 Similarity in Right Triangles 8-1 Similarity in Right Triangles Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.

Holt Geometry 8-1 Similarity in Right Triangles 8-1 Similarity in Right Triangles Holt Geometry Darn!

Use Similar Right Triangles

Ratio and Proportion Students will be able to write and simplify ratios and to use proportions to solve problems.

Similar Right triangles Section 8.1. Geometric Mean The geometric mean of two numbers a and b is the positive number such that a / x = x / b, or:

Chapter 7 Test Review This is to review for your upcoming test Be honest with yourself, can you complete all the problems on you own? HELP!! On successnet,

9-1 Similarity in Right Triangles Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

NOTES GEOMETRIC MEAN / SIMILARITY IN RIGHT TRIANGLES I can use relationships in similar right triangles.

9.3 Similar Right Triangles. Do Now: Draw the altitude and describe what it is.

Date: 10.1(b) Notes: Right Δ Geometric Means Theorem Lesson Objective: Solve problems involving relationships between parts of a right triangle and the.

Section 7-4 Similarity in Right Triangles. Hands-On Activity Take a piece of paper and cut out a right triangle. Use the edge of the paper for the right.

EXAMPLE 3 Use a geometric mean

Warm-up: There is nothing in your folders!

Warm Up 1. Write a similarity statement comparing the two triangles.

Geometric Mean 7.1.

Right Triangles and Trigonometry

Similarity in Right Triangles

Similarity in Right Triangles

8-1: Similarity in Right Triangles

Chapter 7.3 Notes: Use Similar Right Triangles

Similarity in Right Triangles

Objectives Use geometric mean to find segment lengths in right triangles. Apply similarity relationships in right triangles to solve problems.

9.3 Similarity in Right Triangles

8.1-Similarity in Right Triangles

Class Greeting.

Similarity in Right Triangles

Similarity in Right Triangles

Lesson 50 Geometric Mean.

Similarity in Right Triangles

Similarity in Right Triangles

Apply similarity relationships in right triangles to solve problems.

Objectives Students will learn how to use geometric mean to find segment lengths in right triangles and apply similarity relationships in right triangles.

Similar Right Triangles

Similarity in Right Triangles

Geometry B Chapter 8 Geometric Mean.

Similarity in Right Triangles

9.3 Similarity in Right Triangles

8.1 Geometric Mean The geometric mean between two numbers is the positive square root of their product. Another way to look at it… The geometric mean is.

Using Similar Right Triangles

Warm Up Lesson Presentation Lesson Quiz.

BELLWORK 1. Write a similarity statement comparing the two triangles.

Similar Right Triangles

Similarity in Right Triangles

Section 8.1 – 8.2 Geometric Mean Pythagorean Theorem

Similarity in Right Triangles

Similarity in Right Triangles

Similarity in Right Triangles

Presentation transcript:

8-1 Vocabulary Geometric mean

8-1 Similarity in Right Triangles Geometry

8-1-1 Theorem The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other & to the original triangle. B D C A

Example 1 Write a similarity statement comparing the 3 triangles. Z V U W

Geometric mean The geometric mean of two positive numbers is the positive square root of their product.

Example 2 Find the geometric mean of each pair of numbers. If necessary, give the answer in simplest radical form. a.) 4 and 25 b.) 5 and 30

Geometric Mean Corollaries 8-1-2 Corollary The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the two segments of the hypotenuse.

Geometric Mean Corollaries 8-1-3 Corollary The length of a leg of a right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse & the segment of the hypotenuse adjacent to the leg.

Example 3 Find x, y & z. x 9 y 6 z

Ex. 4 To estimate the height of a Douglas fir, Jan positions herself so that her lines of sight to the top & bottom of the tree form a 90° angle. Her eyes are about 1.6 m above the ground, and she is standing 7.8 m from the tree. What is the height of the tree to the nearest meter?