Sections 6.3 & 6.4 Proving triangles are similar using AA, SSS, SAS

Slides:

Advertisements

Similar presentations

7.4 A Postulate for Similar Triangles. We can prove that 2 triangles are similar by showing that all 3 corresponding angles are congruent, and all 3 sides.

Advertisements

Similarity & Congruency Dr. Marinas Similarity Has same shape All corresponding pairs of angles are congruent Corresponding pairs of sides are in proportion.

Honors Geometry Section 8.3 Similarity Postulates and Theorems.

7-3 Proving Triangles Similar

Using Proportions to Solve Geometry Problems Section 6.3.

Triangles and Lines – Congruent Triangles Congruent triangles are triangles that share equal corresponding parts.

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

8-3 Proving Triangles Similar M11.C B

SIMILARITY: A REVIEW A REVIEW Moody Mathematics. Midsegment: a segment that joins the midpoints of 2 sides of a triangle? Moody Mathematics.

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

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

Warm-Up If ∆QRS  ∆ZYX, identify all 3 pairs of congruent angles and all 3 pairs of congruent sides.

Warm Up Solve each proportion If ∆QRS ~ ∆XYZ, identify the pairs of congruent angles and write 3 proportions using pairs of corresponding.

4.4 Proving Triangles are Congruent: ASA and AAS Geometry.

Date: Topic: Proving Triangles Similar (7.6) Warm-up: Find the similarity ratio, x, and y. The triangles are similar. 6 7 The similarity ratio is: Find.

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

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

Warm Up 1.) Find the measure of the exterior angle.

Prove triangles congruent by ASA and AAS

Proving Triangles are Congruent

8.3 Methods of Proving Triangles Similar

7.4 Showing Triangles are Similar: SSS and SAS

Proving Triangles Similar

Proving Triangles are Similar

6.5 – Prove Triangles Similar by SSS and SAS

Similarity Postulates

Take a warm-up from the ChromeBook, calculator, and compass

Proving Triangle Similarity by SSS and SAS

Triangle Congruence HL and AAS

Aim: How do we prove triangles congruent using the Angle-Angle-Side Theorem? Do Now: In each case, which postulate can be used to prove the triangles congruent?

Identify similar triangles Use similar triangles to solve problems

Proving Triangles Congruent

Objective: To use AA, SAS and SSS similarity statements.

Proving Triangles Congruent: SSS and SAS

4-2 Triangle Congruence by SSS and SAS

Other Methods of Proving Triangles Congruent

Three ways to prove triangles congruent.

Some Ways to Prove Triangles Congruent

4-4 and 4-5: Congruent Triangle Theorems

5.3 Proving Triangle Similar

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

Proving Triangles Similar

7-3 Similar Triangles.

4-2 Some Ways to Prove Triangles Congruent (p. 122)

Similarity, Congruence, & Proofs

7-4 and 7-5: Postulates and Theorems for Similar Triangles.

Proving Triangles Similar Related Topic

Triangle Congruence HL and AAS

5.3 Proving Triangle Similar

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

~ ≅ SIMILAR TRIANGLES SIMILAR SAME SHAPE, BUT NOT SAME SIZE CONGRUENT

Geometry Unit 6 Name: _________________________

Proving Triangles Similar.

8.3 Methods of Proving Triangles Similar

APK…..5 minute check.

6.5 – Prove Triangles Similar by SSS and SAS

6.5 – Prove Triangles Similar by SSS and SAS

Proving Triangles Similar.

Week 5 Warm Up Add theorem 2.1 here next year.

Objective We will analyze congruent triangles

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/

Proving Triangles are Congruent

4-4/4-5 Proving Triangles Congruent

Proving Triangles Congruent

8.3 Methods of Proving Triangles are Similar Advanced Geometry 8.3 Methods of Proving    Triangles are Similar Learner Objective: I will use several.

4-2 Triangle congruence by sss & sas

Module 16: Lesson 4 AA Similarity of Triangles

Presentation transcript:

Sections 6.3 & 6.4 Proving triangles are similar using AA, SSS, SAS Geometry Sections 6.3 & 6.4 Proving triangles are similar using AA, SSS, SAS Objective: SWBAT use the AA, SSS, SAS similarity postulates.

Angle- Angle (AA) Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. A ABC ~ DEF because A D and B E D B C E F

Side-Side-Side (SSS) Similarity If the corresponding side lengths of two triangles are proportional, then the triangles are similar. ABC ~ DEF because A D 6 4 8 12 B C 5 E 10 F

Side-Angle-Side (SAS) Similarity If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar. A ABC ~ DEF because B E, D 10 15 B C 12 E 18 F

Example 1:

Example 2:

Example 3:

Example 4: