9.3 Altitude-On-Hypotenuse Theorems (a.k.a Geometry Mean)

Slides:

Advertisements

Similar presentations

8-1 Similarity in Right Triangles

Advertisements

Geometric Mean Theorem I

9.1 Similar Right Triangles. Theorem If an altitude is drawn to the hypotenuse of a Right triangle, then it makes similar triangles to the original Right.

7.1 Geometric Mean.  Find the geometric mean between two numbers  Solve problems involving relationships between parts of right triangles and the altitude.

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.

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

Chapter 7 Jeopardy Game By:Kyle, Yash, and Brahvan.

Geometric Mean & the Pythagorean Thm. Section 7-1 & 7-2.

Similar Right Triangles

Similar Right Triangles 1. When we use a mirror to view the top of something…….

7.4 Similarity in Right Triangles

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

9.3 Altitude-On-Hypotenuse Theorems Objective: After studying this section, you will be able to identify the relationships between the parts of a right.

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.

Similarity in Right Triangles

Geometry 8.1 Right Triangles.

7.4 Similarity in Right Triangles

Honors Geometry Warm-up 1/30 Ashwin is watching the Super Bowl on a wide screen TV with dimensions 32” by 18” while Emily is watching it on an old square.

Chapter 7.4.  The altitude is the Geometric Mean of the Segments of the Hypotenuse.

8.4: Similarity in Right Triangles Objectives: Students will be able to… Find the geometric mean between 2 numbers Find and use relationships between similar.

Geometric and Arithmetic Means

Right Triangles and Trigonometry Chapter Geometric Mean  Geometric mean: Ex: Find the geometric mean between 5 and 45 Ex: Find the geometric mean.

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.

Similar Right Triangle Theorems Theorem 8.17 – If the altitude is drawn to the hypotenuse if a right triangle, then the two triangles formed are similar.

Geometric Mean and the Pythagorean Theorem

To find the geometric mean between 2 numbers

7.3 Use Similar Right Triangles

Warm Up. 9.4 Geometry’s Most Elegant Theorem Pythagorean Theorem.

Chapter 7 Similarity.

Use Similar Right Triangles

Warm-up On a blank piece of paper compute the following perfect squares.. xx2x ……

Pythagorean Theorem Advanced Geometry Trigonometry Lesson 1.

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:

9.3 Altitude-On-Hypotenuse Theorems (a.k.a Geometry Mean)

Warm-up: Simplify 1) 1) 2) 2) 3) 3). A C B D 9.1 – Exploring Right Triangles Theorem 9.1 – If an altitude is drawn to the hypotenuse of a right triangle,

9.1 Similar Right Triangles Geometry. Objectives  Solve problems involving similar right triangles formed by the altitude drawn to the hypotenuse of.

7.4 Notes Similarity in Right Triangles. Warm-up:

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.

Geometry 6.4 Geometric Mean.

Lesson 7.3 Using Similar Right Triangles Students need scissors, rulers, and note cards. Today, we are going to… …use geometric mean to solve problems.

Key Learning  Solve problems involving similar right triangles formed by the altitude drawn to the hypotenuse of a right triangle.  Use a geometric mean.

9.1 Similar Right Triangles Geometry Mrs. Blanco.

8-1 Geometric Mean The student will be able to: 1.Find the geometric mean between two numbers. 2.Solve problems involving relationships between parts of.

Geometric Mean 7.1.

Right Triangles and Trigonometry

Geometric Mean Pythagorean Theorem Special Right Triangles

Theorem The area A of a triangle is

Pearson Unit 3 Topic 9: Similarity 9-4: Similarity in Right Triangles Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007.

Similar Right Triangles

X = 3 y = 6 r = 3 y = 20.

9.1 Similar Right Triangles

5.4: The Pythagorean Theorem

Chapter 7.3 Notes: Use Similar Right Triangles

Similar Right Triangles: Geometric Mean

9.3 Warmup Find the value of x and y

9.3 Altitude-On-Hypotenuse Theorems

Lesson 50 Geometric Mean.

Altitudes–On- Hypotenuse Theorem

Similar Right Triangles

5.4: The Pythagorean Theorem

Chapter 8 Section 1 Recall the rules for simplifying radicals:

Geometric Mean Pythagorean Theorem Special 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

Geometric Mean and the Pythagorean Theorem

Midpoint and Median P9. The midpoint of the hypotenuse of a right triangle is equidistant from the 3 vertices. P12. The length of a leg of a right triangle.

Similar Right Triangles

Right Triangles with an altitude drawn.

Presentation transcript:

9.3 Altitude-On-Hypotenuse Theorems (a.k.a Geometry Mean)

When an altitude is drawn from to a hypotenuse then three similar triangles are formed. Identify the three similar triangles! Which theorem can they be proven similar?

Remember: Given two numbers a and b, x is the geometric mean if MEANS EXTREMES

Find the geometric mean of 9 and 16

A B C Altitudes!!!! What do you remember? An Altitude *Starts at a vertex *Forms a right angle D

A B C The hypotenuse is split into two pieces BD and DA D CD (the altitude) is the geometric mean of those two pieces

A B C D If the altitude is in the means place, put the two segments of the hypotenuse into the extremes.

the LEG is the geometric mean A BC D If the leg is in the means place, put the whole hyp. and segment closest to that leg into the extremes. AB AC AD

the LEG is the geometric mean A BC D AB CB BD

A B C D 9 16 x EX: 1 Find x x x9 16

EX: 2 Find the length of AB. A BC D 32 15

A B C D 3 x 4 EX 3: Solve for x

EX: 4 Find the length of CB. A B C D x x = 40

A B C D x 12 5 EX: 5 Solve for x