Presentation is loading. Please wait.

Presentation is loading. Please wait.

Introduction When a series of similarity transformations are performed on a triangle, the result is a similar triangle. When triangles are similar, the.

Published byCori Randall Modified over 6 years ago

Similar presentations

Presentation on theme: "Introduction When a series of similarity transformations are performed on a triangle, the result is a similar triangle. When triangles are similar, the."— Presentation transcript:

1 Introduction When a series of similarity transformations are performed on a triangle, the result is a similar triangle. When triangles are similar, the corresponding angles are congruent and the corresponding sides are of the same proportion. It is possible to determine if triangles are similar by measuring and comparing each angle and side, but this can take time. There exists a set of similarity statements, similar to the congruence statements, that let us determine with less information whether triangles are similar. 1.6.2: Applying Similarity Using the Angle-Angle (AA) Criterion

2 Key Concepts The Angle-Angle (AA) Similarity Statement is one statement that allows us to prove triangles are similar. The AA Similarity Statement allows that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. 1.6.2: Applying Similarity Using the Angle-Angle (AA) Criterion

3 Key Concepts, continued
Notice that it is not necessary to show that the third pair of angles is congruent because the sum of the angles must equal 180˚. Similar triangles have corresponding sides that are proportional. The Angle-Angle Similarity Statement can be used to solve various problems, including those that involve indirect measurement, such as using shadows to find the height of tall structures. 1.6.2: Applying Similarity Using the Angle-Angle (AA) Criterion

4 Common Errors/Misconceptions
misidentifying congruent parts because of the orientation of the triangles misreading similarity statements as congruent statements incorrectly creating proportions between corresponding sides 1.6.2: Applying Similarity Using the Angle-Angle (AA) Criterion

5 Guided Practice Example 2 Explain why , and then find the length of
1.6.2: Applying Similarity Using the Angle-Angle (AA) Criterion

6 Guided Practice: Example 2, continued
Show that the triangles are similar. According to the diagram, and by the Angle-Angle (AA) Similarity Statement. 1.6.2: Applying Similarity Using the Angle-Angle (AA) Criterion

7 Guided Practice: Example 2, continued Find the length of .
Corresponding sides of similar triangles are proportional. Create and solve a proportion to find the length of 1.6.2: Applying Similarity Using the Angle-Angle (AA) Criterion

8 Guided Practice: Example 2, continued The length of is 5.52 units.
Corresponding sides are proportional. Substitute known values. Let x represent the length of (2.72)(6.9) = (3.4)(x) Solve for x. = 3.4x x = 5.52 ✔ 1.6.2: Applying Similarity Using the Angle-Angle (AA) Criterion

9 Guided Practice: Example 2, continued
1.6.2: Applying Similarity Using the Angle-Angle (AA) Criterion

10 Guided Practice Example 4
Suppose a person 5 feet 10 inches tall casts a shadow that is 3 feet 6 inches long. At the same time of day, a flagpole casts a shadow that is 12 feet long. To the nearest foot, how tall is the flagpole? 1.6.2: Applying Similarity Using the Angle-Angle (AA) Criterion

11 Guided Practice: Example 4, continued Identify the known information.
The height of a person and the length of the shadow cast create a right angle. The height of the flagpole and the length of the shadow cast create a second right angle. You can use this information to create two triangles. Draw a picture to help understand the information. 1.6.2: Applying Similarity Using the Angle-Angle (AA) Criterion

12 Guided Practice: Example 4, continued
1.6.2: Applying Similarity Using the Angle-Angle (AA) Criterion

13 Guided Practice: Example 4, continued
Determine if the triangles are similar. Two pairs of angles are congruent. According to the Angle-Angle (AA) Similarity Statement, the triangles are similar. Corresponding sides of similar triangles are proportional. 1.6.2: Applying Similarity Using the Angle-Angle (AA) Criterion

14 Guided Practice: Example 4, continued
Find the height of the flagpole. Create and solve a proportion to find the height of the flagpole. 1.6.2: Applying Similarity Using the Angle-Angle (AA) Criterion

15 Guided Practice: Example 4, continued The flagpole is 20 feet tall.
Corresponding sides are proportional. Let x represent the height of the flagpole. Simplify. Solve for x. x = 20 ✔ 1.6.2: Applying Similarity Using the Angle-Angle (AA) Criterion

16 Guided Practice: Example 4, continued
1.6.2: Applying Similarity Using the Angle-Angle (AA) Criterion

Download ppt "Introduction When a series of similarity transformations are performed on a triangle, the result is a similar triangle. When triangles are similar, the."

Similar presentations

Objective: After studying this section, you will be able to use the concept of similarity to establish the congruence of angles and the proportionality.

Objective: After studying this section, you will be able to use the concept of similarity to establish the congruence of angles and the proportionality.
Prove Triangles Similar by AA 6.4. Another Postulate All you need are any 2 congruent angles for 2 triangles to be congruent.

Prove Triangles Similar by AA 6.4. Another Postulate All you need are any 2 congruent angles for 2 triangles to be congruent.
Bellwork Solve Solve Solve for x Solve for x Two similar triangles have a scale factor of 2. The sum of the angles in the first triangle is 180 o. What.

Bellwork Solve Solve Solve for x Solve for x Two similar triangles have a scale factor of 2. The sum of the angles in the first triangle is 180 o. What.
Introduction Geometry includes many definitions and statements. Once a statement has been shown to be true, it is called a theorem. Theorems, like definitions,

Introduction Geometry includes many definitions and statements. Once a statement has been shown to be true, it is called a theorem. Theorems, like definitions,
Introduction If a rigid motion or a series of rigid motions, including translations, rotations, or reflections, is performed on a triangle, then the transformed.

Introduction If a rigid motion or a series of rigid motions, including translations, rotations, or reflections, is performed on a triangle, then the transformed.
Introduction There are many ways to show that two triangles are similar, just as there are many ways to show that two triangles are congruent. The Angle-Angle.

Introduction There are many ways to show that two triangles are similar, just as there are many ways to show that two triangles are congruent. The Angle-Angle.
Introduction Design, architecture, carpentry, surveillance, and many other fields rely on an understanding of the properties of similar triangles. Being.

Introduction Design, architecture, carpentry, surveillance, and many other fields rely on an understanding of the properties of similar triangles. Being.
Introduction Congruent triangles have corresponding parts with angle measures that are the same and side lengths that are the same. If two triangles are.

Introduction Congruent triangles have corresponding parts with angle measures that are the same and side lengths that are the same. If two triangles are.
JRLeon Geometry Chapter 11.3 HGSH Lesson 11.3 (603) Suppose I wanted to determine the height of a flag pole, but I did not have the tools necessary. Even.

JRLeon Geometry Chapter 11.3 HGSH Lesson 11.3 (603) Suppose I wanted to determine the height of a flag pole, but I did not have the tools necessary. Even.
EXAMPLE 3 Standardized Test Practice.

EXAMPLE 3 Standardized Test Practice.
EXAMPLE 3 Standardized Test Practice. EXAMPLE 3 Standardized Test Practice SOLUTION The flagpole and the woman form sides of two right triangles with.

EXAMPLE 3 Standardized Test Practice. EXAMPLE 3 Standardized Test Practice SOLUTION The flagpole and the woman form sides of two right triangles with.
8.3: Proving Triangles Similar

8.3: Proving Triangles Similar
3.4: Using Similar Triangles

3.4: Using Similar Triangles
Thales is known as the first Greek scientist, engineer, and mathematician. Legend says that he was the first to determine the height of the pyramids.

Thales is known as the first Greek scientist, engineer, and mathematician. Legend says that he was the first to determine the height of the pyramids.
1. In ABC and XZW, m A = m X and m B = m Z

1. In ABC and XZW, m A = m X and m B = m Z
 Then: You used AAS, SSS, and SAS Congruence Theorems to prove triangles congruent.  Now: 1. Identify similar triangles using the AA Similarity Postulate.

 Then: You used AAS, SSS, and SAS Congruence Theorems to prove triangles congruent.  Now: 1. Identify similar triangles using the AA Similarity Postulate.
Station 1 - Proportions Solve each proportion for x. 1. 2. 3. 4. 5. 6.

Station 1 - Proportions Solve each proportion for x
8.5 Proving Triangles are Similar. Side-Side-Side (SSS) Similarity Theorem If the lengths of the corresponding sides of two triangles are proportional,

8.5 Proving Triangles are Similar. Side-Side-Side (SSS) Similarity Theorem If the lengths of the corresponding sides of two triangles are proportional,
When a 6-ft student casts a 17-ft shadow, a flagpole casts a shadow that is 51 ft long. Find the height of the flagpole. Similarity and Indirect Measurement.

When a 6-ft student casts a 17-ft shadow, a flagpole casts a shadow that is 51 ft long. Find the height of the flagpole. Similarity and Indirect Measurement.
Introduction Geometry includes many definitions and statements. Once a statement has been shown to be true, it is called a theorem. Theorems, like definitions,

Introduction Geometry includes many definitions and statements. Once a statement has been shown to be true, it is called a theorem. Theorems, like definitions,

Similar presentations

Ads by Google