Warm Up P NMRB W ∆PRB~ ∆WNM PR = 20 PB =18RB = 22WN =12 Find NM and WM 20/12 = 18/WM = 22/NM WM = 10.8 and NM = 13.2.

Slides:

Advertisements

Similar presentations

Proving Triangles Congruent

Advertisements

Proving Triangles Congruent

Hypotenuse – Leg Congruence Theorem: HL

6-2: Proving Congruence using congruent parts Unit 6 English Casbarro.

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

4-4 & 4-5: Tests for Congruent Triangles

Proving Triangles Congruent Advanced Geometry Triangle Congruence Lesson 2.

WARM UP 1)List the six congruencies if the following is true. 2)Plot the points and locate point C so that F(7,5) A(-2,2) T(5,2)

4.3 & 4.4 Proving Triangles are Congruent

Chapter 4 Congruent Triangles.

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

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

7-3 Proving Triangles Similar

Proving Triangles Congruent. Warm Up Objectives Can you prove triangles congruent using SSS, SAS, ASA, AAS, and HL?

Do Now #28:. 5.4 Hypotenuse-Leg (HL) Congruence Theorem Objective: To use the HL Congruence Theorem and summarize congruence postulates and theorems.

Proving Triangles Congruent

DO NOW!!! Solve for “x”..

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

Methods of Proving Triangles Similar Lesson 8.3. Postulate: If there exists a correspondence between the vertices of two triangles such that the three.

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

Triangle Congruence. 3 line segments (dried spaghetti sticks – make three different sizes) Take 3 line segments Make a triangle Mark the vertices Draw.

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:

Then/Now You proved triangles congruent using the definition of congruence. Use the SSS Postulate to test for triangle congruence. Use the SAS Postulate.

Unit 2 Part 4 Proving Triangles Congruent. Angle – Side – Angle Postulate If two angles and the included side of a triangle are congruent to two angles.

Warm Up  For both right triangles, find the value of x. x x

Triangle Similarity Keystone Geometry. 2 Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding.

4.5 – Prove Triangles Congruent by ASA and AAS In a polygon, the side connecting the vertices of two angles is the included side. Given two angle measures.

Proving Triangles are Congruent: SSS and SAS Sec 4.3

4-3 Triangle Congruence by ASA and AAS. Angle-Side-Angle (ASA) Postulate If two angles and the included side of one triangle are congruent to two angles.

5.6 Proving Triangle Congruence by ASA and AAS. OBJ: Students will be able to use ASA and AAS Congruence Theorems.

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.

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)

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.

Objectives Apply ASA, AAS, and HL to construct triangles and to solve problems. Prove triangles congruent by using ASA, AAS, and HL.

Triangle Proofs. USING SSS, SAS, AAS, HL, & ASA TO PROVE TRIANGLES ARE CONGRUENT STEPS YOU SHOULD FOLLOW IN PROOFS: 1. Using the information given, ______________.

Triangle Congruence Theorems

Prove triangles congruent by ASA and AAS

Geometry-Part 7.

Proving Triangles are Congruent

8.3 Methods of Proving Triangles Similar

Proving Triangles Congruent

Triangle Congruence HL and AAS

5.3 Proving Triangles are congruent:

Proving Triangles Congruent: SSS and SAS

Other Methods of Proving Triangles Congruent

Proving Triangles Congruent

Three ways to prove triangles congruent.

4-4 and 4-5: Congruent Triangle Theorems

5.3 Proving Triangle Similar

Warm-Up Determine if the following triangles are congruent and name the postulate/definitions/properties/theorems that would be used to prove them congruent.

Proving Triangles Similar

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

Warm Up ∆PRB~ ∆WNM PR = 20 PB =18 RB = 22 WN =12 Find NM and WM

Triangle Congruence HL and AAS

Identifying types and proofs using theorems

8.3 Methods of Proving Triangles Similar

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

(AAS) Angle-Angle-Side Congruence Theorem

Proving Triangles are Congruent

Methods of Proving Triangles Similar

Warm Up 7.4 Is there enough information to prove that the triangles are congruent? If so, state the reason (SSS, SAS, HL, ASA,

Warm Up 1 ( Write a congruence statement

4-4/4-5 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.

Presentation transcript:

Warm Up P NMRB W ∆PRB~ ∆WNM PR = 20 PB =18RB = 22WN =12 Find NM and WM 20/12 = 18/WM = 22/NM WM = 10.8 and NM = 13.2

8.3 Methods of proving triangles similar

Postulate: If there exists a correspondence between the vertices of two triangles such that the three angles of one triangle are congruent to the corresponding angles of the other triangle, then the triangles are similar. (AAA) The following 3 theorems will be used in proofs much as SSS, SAS, ASA, HL and AAS were used in proofs to establish congruency.

T62: If there exists a correspondence between the vertices of two triangles such that two angles of one triangle are congruent to the corresponding angles of the other, then the triangles are similar. (AA) (no choice) T63: If there exists a correspondence between the vertices of two triangles such that the ratios of the measures of corresponding sides are equal, then the triangles are similar. (SSS~)

T64: If there exists a correspondence between the vertices of two triangles such that the ratios of the measures of two pairs of corresponding sides are equal and the included angles are congruent, then the triangles are similar. (SAS~)

Given: ABCD is a Prove: ∆BFE ~ ∆ CFD A C D B F E (AA)

Given: LP  EA; N is the midpoint of LP. P and R trisect EA. Prove: ∆PEN ~ ∆PAL SAS ~ A E N L PR