DO NOW.

Slides:



Advertisements
Similar presentations
8-1 Similarity in Right Triangles
Advertisements

SIMILARITIES IN A RIGHT TRIANGLE
Similarity in Right Triangles
HL Postulate Lesson 3.8.
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.
Mean Proportional – Day 2
Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles.
Similar Right Triangles
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.
A B C D Lesson 9.3. AB D C A D C B D A C B Three similar triangles: small, medium and large. Altitude CD drawn to hyp. of △ ABC Three similar triangles.
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
7.4 Similarity in Right Triangles
Mean Proportional.
7-4 Similarity in Right Triangles
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 Mean and Right Triangles
9.3 Altitude-On-Hypotenuse Theorems (a.k.a Geometry Mean)
Geometric and Arithmetic Means
A = B SECTION 7-1 Jim Smith JCHS. The Geometric Mean Between 2 Numbers ( A and B ), Is The Number That When Substituted For X Will Make This Proportion.
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 Triangles
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.
Chapter 8 Lesson 4 Objective: To find and use relationships in similar right triangles.
Section 8-1: Geometric Mean When the means of a proportion are the same number, that number is called the geometric mean of the extremes.
To find the geometric mean between 2 numbers
7.3 Use Similar Right Triangles
Chapter 7 Similarity.
Warm Up 1.Name a chord 2.What term describes
Use Similar Right Triangles
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)
9.3 Similar Right Triangles. Do Now: Draw the altitude and describe what it is.
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.
 Lesson 7-4.  Draw one of the diagonals for your rectangle to form two right triangles. Q: What is the relationship between the two right triangles?
Find the geometric mean between: 1.6 and and 20 Geometric Mean x is the geometric mean between a and b. a x x b = Warm-up!!
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.
Geometric Mean 7.1.
Right Triangles and Trigonometry
Triangle Segments.
8.1: Geometric Mean Day 2.
8-1: Similarity in Right Triangles
9.1 Similar Right Triangles
Chapter 7.3 Notes: Use Similar Right Triangles
Similar Right Triangles: Geometric Mean
7.3 Use Similar Right Triangles
9.3 Altitude-On-Hypotenuse Theorems
Lesson 50 Geometric Mean.
Use Similar Right Triangles
Altitudes–On- Hypotenuse Theorem
Similar Right Triangles
Similar Right Triangles
Chapter 8 Section 1 Recall the rules for simplifying radicals:
RIGHT TRIANGLE PROPORTIONS
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
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:

DO NOW

Geometric Means in Right Triangles

C A D B C C D B A D

C A B C C D B A D

The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse. 𝑨𝑫 𝑪𝑫 = 𝑪𝑫 𝑫𝑩

ALTITUDE RULE The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse.

X = 𝟏 𝟐 𝑥 2 = 2 8 X =𝟐𝟕 3 9 = 9 𝑥 40 𝑥 = 𝑥 10 X =𝟐𝟎

AB CB The leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse. = CB DB Leg Rule

AB CA The leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse. = CA AD Leg Rule

X = 6 9 𝑥 = 𝑥 4 X = 2 𝟕𝟎 20 𝑥 = 𝑥 14 X = 100 𝑥 60 = 60 36

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2025 SlidePlayer.com. Inc. All rights reserved.