~adapted from Walch Education PROVING TRIANGLE SIMILARITY USING SAS AND SSS SIMILARITY.

Slides:

Advertisements

Similar presentations

Proving Triangles Congruent: SSS and SAS

Advertisements

Section 4-3 Triangle Congruence (ASA, AAS) SPI 32C: determine congruence or similarity between triangles SPI 32M: justify triangle congruence given a diagram.

Congruent Polygons. Congruent segments have the same length.

Proving Triangles Congruent Advanced Geometry Triangle Congruence Lesson 2.

4-2: Triangle Congruence by SSS and SAS 4-3: Triangle Congruence by ASA and AAS 4-4: Using Corresponding Parts of Congruent Triangles.

6.3 Congruent Triangles: SSS and SAS

Mrs. Rivas 1. three pairs of congruent sides 2. three pairs of congruent angles.

8.5 Proving Triangles Similar

2.11 – SSS, SAS, SSA.

Similarity in Triangles. Similar Definition: In mathematics, polygons are similar if their corresponding (matching) angles are congruent (equal in measure)

Honors Geometry Section 8.3 Similarity Postulates and Theorems.

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.

~adapted by Walch Education  The Pythagorean Theorem is often used to find the lengths of the sides of a right triangle, a triangle that includes one.

7-3 Proving Triangles Similar. Triangle Similarity Angle-Angle Similarity Postulate: If two angles of one triangle are congruent to two angles of another.

7-3 Proving Triangles Similar

Thursday, January 10, 2013 A B C D H Y P E. Homework Check.

Lesson: 9 – 3 Similar Triangles

Working with Ratio Segments PART 1 ~adapted from Walch Education.

Name all the things that can you conclude from each diagram? things2. 3 things3.4 things Warm Up.

Triangle Congruence: by SSS and SAS Geometry H2 (Holt 4-5) K. Santos.

Chapter 4: Triangle Congruence MISSY MCCARTHY OKEMOS HIGH SCHOOL MATH INSTRUCTOR.

8-3 Proving Triangles Similar Learning Target: I will be able to prove triangles are similar. Goal 2.03.

Monday, October 22, 2012 Homework: p. 211 #28-34 even.

4.4 – Prove Triangles Congruent by SAS Geometry Ms. Rinaldi.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Warm up 1.What is the ratio of the corresponding side lengths for two congruent triangles?

(AA, SSS, SAS). AA Similarity (Angle-Angle) If 2 angles of one triangle are congruent to 2 angles of another triangle, then the triangles are similar.

Geometry Sections 6.4 and 6.5 Prove Triangles Similar by AA Prove Triangles Similar by SSS and SAS.

Prove Triangles Similar by SSS and SAS

DEFINING SIMILARITY ~ADAPTED FROM WALCH EDUCATION.

8-3 Proving Triangles Similar M11.C B

Question about homework? Any questions on the homework? (choose random problems)

4-2 Triangle Congruence by SSS and SAS. Side-Side-Side (SSS) Postulate If the three sides of one triangle are congruent to the three sides of another.

Drill Write your homework in your planner Take out your homework Find all angle measures:

4.2: Triangle Congruency by SSS and SAS

U W VX Z Y XYZ 5/ Warm Up.

 There are 3 ways to show two triangles are similar to each other. Those 3 ways are: 1. Angle-Angle Similarity Postulate. (AA~) 2. Side-Angle-Side Similarity.

Proving Congruence – SSS, SAS Side-Side-Side Congruence Postulate (SSS) If the sides of one triangle are congruent to the sides of a second triangle, then.

Proving Triangles are Congruent: SSS and SAS Sec 4.3

4. 1 Apply Congruence and Triangles 4

Proving Congruence SSS, SAS Postulate 4.1 Side-Side-Side Congruence If the sides of one triangle are congruent to the sides of a second triangle, then.

DO NOW Identify the corresponding parts using tick marks. Then state which polygons are congruent. 1.2.

Geometry: Similar Triangles. MA.912.G.4.5 Apply theorems involving segments divided proportionally Block 28.

Warm Up Check homework answers with each other!. Answers 4.1 c worksheet.

4.2 Triangle Congruence by SSS and SAS You can prove that two triangles are congruent without having to show that all corresponding parts are congruent.

Geometry Sections 4.3 & 4.4 SSS / SAS / ASA

Triangle Congruence by SSS & SAS Objective: To Determine whether triangles are congruent using SSS and SAS postulate.

Proving Triangle Congruency. What does it mean for triangles to be congruent? Congruent triangles are identical meaning that their side lengths and angle.

Section Review Triangle Similarity. Similar Triangles Triangles are similar if (1) their corresponding (matching) angles are congruent (equal)

5.2 Proving Triangles are Congruent: SSS and SAS Textbook pg 241.

Chapter 9, Section 5 Congruence. To be congruent: –corresponding parts (sides/ angles) have the same measure.

 Students will apply the SSS & SAS Similarity Theorems to determine similarity in triangles.  Why? So you can show that triangles are similar, as seen.

4-4 Using Corresponding Parts of Congruent Triangles I can determine whether corresponding parts of triangles are congruent. I can write a two column proof.

4.2 Notes SSS and SAS. What can you conclude? Look at the diagram. What can you conclude, if anything? How can you justify your conclusion(s).

Congruent Triangles Featuring SSS and SAS (side-side-side and side-angle-side)

Proving Side-Side-Side. Proving Side-Angle-Side Create a 55 ° angle. Its two sides should be 3.5 and 5 inches long. Enclose your angle to make a triangle.

5.2 Proving Triangles are Congruent by SSS and SAS

Z Warm Up W U 5 V X Y 6 XYZ 5/

7-3 Similar Triangles.

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.

Applying Similarty Using the Angle-angle (AA) criterions

Proving Triangles Similar.

Explaining SAS, ASA, and SSS

Proving Triangles Similar.

Postulates and Theorems to show Congruence SSS: Side-Side-Side

Similar Similar means that the corresponding sides are in proportion and the corresponding angles are congruent. (same shape, different size)

6-3/6-4: Proving Triangles Similar

Z Warm Up W U 5 V X Y 6 XYZ 5/

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.

~ Adapted from Walch Education

Presentation transcript:

~adapted from Walch Education PROVING TRIANGLE SIMILARITY USING SAS AND SSS SIMILARITY

 If the measures of two sides of a triangle are proportional to the measures of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar. SIDE-ANGLE-SIDE (SAS) SIMILARITY STATEMENT

 If the measures of the corresponding sides of two triangles are proportional, then the triangles are similar. SIDE-SIDE-SIDE (SSS) SIMILARITY STATEMENT

A proof is a set of justified statements organized to form a convincing argument that a given statement is true. Definitions, algebraic properties, and previously proven statements can be used to prove a given statement.  There are several types of proofs, such as paragraph proofs, two-column proofs, and flow diagrams.  Every good proof includes step-by-step statements that support your reasoning PROOFS

Determine whether the triangles are similar. Explain your reasoning. PRACTICE # 1 According to the diagram Compare the side lengths: If the triangles are similar, then the corresponding sides are proportional. The side lengths are proportional. by the Side-Angle-Side (SAS) Similarity Statement.

~ Ms. Dambreville THANKS FOR WATCHING!