Similarity in Right Triangles

Dec 17, 2025

260 likes | 386 Views

This article explores the concept of similarity in right triangles, highlighting how two triangles are similar if their corresponding angles are equal and their sides are in proportion. We delve into the conditions for similarity, including the Angle-Angle (AA) criterion, and the applications of these principles in various mathematical problems and real-world scenarios. Examples and visual aids help illustrate the key concepts, providing a deeper understanding of similarity and its importance in geometry.

Share Presentation

Embed Code

inga

Download Presentation

Similarity in Right Triangles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

8-4 Similarity in Right Triangles

8-4 Similarity in Right Triangles. One Key Term One Theorem Two Corollaries. Theorem 8-3. Altitude Similarity Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. C. A. B. D.

499 views • 7 slides

Similarity in Right Triangles

Chapter 7.4. Similarity in Right Triangles. Right Triangles. Leg. Leg. Altitude. Hypotenuse. The altitude is the Geometric Mean of the Segments of the Hypotenuse. Leg. Leg. Altitude. Short segment. Long segment. Short seg. =. Alt. Use the formula:. Alt. Long seg. Leg. Leg.

660 views • 31 slides

8.4: Similarity in Right Triangles

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 right triangles. Geometric Mean:. In a proportion, , b and c are called the “means”

2k views • 10 slides

Section 7-4 Similarity in Right Triangles

Section 7-4 Similarity in Right Triangles. Objectives: Find and use relationships in right triangles. Geometric Mean.

332 views • 7 slides

Geometric Means and Similarity in Right Triangles

Geometric Means and Similarity in Right Triangles. Warm-ups. Geometric Means. The geometric mean of two numbers is the positive square root of their product. Example 1: Find the geometric mean of 5 and 20 Example 2: Find the geometric mean of 3 and 6. Similarity in Right Triangles.

251 views • 8 slides

Similarity in Right Triangles

Similarity in Right Triangles. 7-4. Warmup activity (don’t need to turn in). Complete activity on p. 391 with a partner. Theorem. In a right triangle, the altitude to the hypotenuse yields three similar triangles. B. A. C. D. Example. b. a. e. c. d. f. b. f. a. a. e. d. c.

295 views • 12 slides

Similarity in Right Triangles

Similarity in Right Triangles. Geometry CP2 (Holt 8-1) K. Santos. Parts of a Right Triangle. A B C Hypotenuse—side opposite the right angle Legs—sides that form the right angle and . Altitude to the Hypotenuse. X

468 views • 10 slides

Right Triangles

Right Triangles. The Trig Ratios. Brought to you by Moody Mathematics. Let’s review some vocabulary. Moody Mathematics. A. Hypotenuse. C. B. Moody Mathematics. Opposite Leg. A. C. B. Opposite Leg to A. Moody Mathematics. Opposite Leg. Opposite Leg to B. B. Moody Mathematics. A.

916 views • 64 slides

8-1 Similarity in Right Triangles

8-1 Similarity in Right Triangles. 2/19/13. Bell Work. 1. Write a similarity statement comparing the two triangles. Simplify. 2. 3. Solve each equation. 4. 5. 2 x 2 = 50. ∆ ADB ~ ∆ EDC. ±5. Theorem 1.

374 views • 16 slides

Geometry Similarity in Right Triangles

Geometry Similarity in Right Triangles. Warm up. Find the x- intercept and y-intercept for each equation. 1). 3y + 4 = 6x 2). x + 4 = 2y 3). 3y – 15 = 15x. 1) x- intercept= 2/3 y-intercept =-4/3 2) x- intercept= -4 y-intercept =2 3) x- intercept= 5 y-intercept =-1.

552 views • 28 slides

7-4 Similarity in Right Triangles

7-4 Similarity in Right Triangles. Right Triangle Relationships. Theorem : The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. “Trick” for Identifying the Similar Triangles (NOT IN BOOK!).

661 views • 9 slides

Right Triangles

Right Triangles. Investigate the Chart. Investigate the Chart. Investigate the Chart. (Sin q) 2 + ( Cos q) 2.

124 views • 6 slides

Similarity, Right Triangles, and Trigonometry

Similarity, Right Triangles, and Trigonometry. Clusters: 1. Understand similarity in terms of similarity transformations 2. Prove theorems involving similarity. 3. Define trigonometric ratios and solve problems involving right triangles. 4. Apply trigonometry to general triangles.

567 views • 22 slides

8-1 – Similarity in Right Triangles

8-1 – Similarity in Right Triangles. Objective: Determine the geometric mean between two numbers. Apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle.

254 views • 9 slides

Similarity in Right Triangles

Similarity in Right Triangles. FIRST BIG NOTE!!! (~) Is the symbol for Similarity. Holt McDougal Geometry. Holt Geometry. Warm Up 1. Write a similarity statement comparing the two triangles. Simplify. 2. 3. Solve each equation. 4. 5. 2 x 2 = 50. ∆ ADB ~ ∆ EDC. ±5.

605 views • 25 slides

Similar Right Triangles within Right Triangles

Similar Right Triangles within Right Triangles. OPTIONAL EXTRA CREDIT NOTES. If an altitude (perpendicular line) is drawn from a right angle to the hypotenuse, it makes three similar triangles.

213 views • 8 slides

Right Triangles

Right Triangles Introduction to the Mathematics for Solving Unknown Angles and Leg Lengths of Right Triangles. Lesson Topics. Triangle Classifications Right Triangles Angle Sum Theorem Triangle Congruency Postulates Right Triangle Similarity Theorem Pythagorean Theorem

380 views • 34 slides

Notes Geometric Mean / Similarity in Right Triangles

Notes Geometric Mean / Similarity in Right Triangles. I can use relationships in similar right triangles. Simplifying Radicals. Perfect Squares – 1, 4, 9, 16, 25, 36, 49, 64, 81… Find the largest Perfect Square that goes into the number evenly

190 views • 12 slides

7.4 Similarity in Right 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 in it. Geometric Mean. Before we look at right triangles we will examine something called the GEOMETRIC MEAN.

518 views • 12 slides

More Related