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.

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.
Assignment P. 361: 32, 34, 36 P : 1-3, 5-23, 30, 31, 33, 38, 39 Challenge Problems.
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 ═
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.
7.4 Similarity in Right Triangles
Mean Proportional.
7-4 Similarity in Right Triangles
Section 9.1 Similar Right Triangles OBJECTIVE: To find and use relationships in similar right triangles BIG IDEAS: REASONING AND PROOF VISUALIZATIONPROPORTIONALITY.
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.
9.1 (old geometry book) Similar Triangles
Geometric Mean and Right Triangles
9.3 Altitude-On-Hypotenuse Theorems (a.k.a Geometry Mean)
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 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.
Lesson 7-1 Geometric Means Theorem 7.1 If the altitude is drawn from the vertex of the right angle of a right triangle to its hypotenuse, then the two.
7.3 Use Similar Right Triangles
Similarity in Right Triangles Geometry Unit 11, Day 7 Ms. Reed.
 By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C.
Proportional Parts of a Triangle Proportional Perimeters Theorem If two triangles are similar, then the perimeters are proportional to the measures of.
Chapter 7 Similarity.
Use Similar Right Triangles. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed.
Use Similar Right Triangles
7.1 Ratio and Proportions -Ratios: A comparison of 2 quantities -Proportion: A statement that 2 ratios are equal -Extended Proportion: When 3 or more ratios.
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)
7.3 Use Similar Right Triangles
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.
9.1 Similar Right Triangles Geometry. Objectives  Solve problems involving similar right triangles formed by the altitude drawn to the hypotenuse of.
Section 8-1 Similarity in Right Triangles. Altitudes altitude Recall that an altitude is a segment drawn from a vertex such that it is perpendicular to.
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.
7.4 Notes Similarity in Right Triangles. Warm-up:
Chapter 9: Right Triangles and Trigonometry Section 9.1: Similar Right Triangles.
Chapter 9: Right Triangles and Trigonometry Lesson 9.1: Similar Right Triangles.
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 7-4.  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.
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
8-1: Similarity in Right Triangles
Chapter 7.3 Notes: Use Similar Right Triangles
7.3 Use Similar Right Triangles
Lesson 50 Geometric Mean.
Use Similar Right Triangles
Similar Right Triangles
DO NOW.
Geometric Mean Pythagorean Theorem Special Right Triangles
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:

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 formed are similar to the original right triangle.

How do you names the 3 similar triangles? 1. Draw the smallest triangle. îSUT ~ îTUR 2. Draw the middle triangle. 3. Draw the largest triangle. ~ îSTR 4. Match up the angles.

Name the similar triangles, then find x. îEHG ~ îGHF ~ îEGF To find x make a ratio of the hypotenuses and the a ratio of 2 proportional legs.

Name the similar triangles and find x. îLKM ~ îMKJ ~ îLMJ

Find x and y x y

Find x.

Find x

Theorem 7.6 In a right triangle the altitude from the right angle to the hypotenuse divides the hypotenuse into 2 segments. The length of the altitude is the geometric mean of the lengths of the 2 segments

Finding the length of the altitude B CA D 1.Set up a proportion to find BD. 2.Find side AD. 3.Plug values into

Finding the length of the altitude

Find the amplitude, if these are right triangles. One of these is not a right triangle not right

Theorem 7.7 In a right triangle, the altitude divides the hypotenuse into 2 segments. The length of each leg of each right triangle is the geometric mean of length of the hypotenuse and a segment of the hypotenuse

Find x and y xy

Find x

Find x and y 28 x +2 y

Find a

Find b

Find x and y y x | | 30 z 16

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

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