GEOMETRY Proving Triangles are Congruent: ASA and AAS.

Slides:

Advertisements

Similar presentations

4.5 Proving Δs are  : ASA and AAS & HL

Advertisements

Proving Δs are  : SSS, SAS, HL, ASA, & AAS

Triangle Proofs J E T M. State the reason for each statement: J E T M Given: E is the midpoint of MJ. TE MJ. Prove: MET JET Statements: 1. E is the midpoint.

Proving Triangles are Congruent SSS, SAS; ASA; AAS

4.5 Proving Δs are  : ASA and AAS. Objectives: Use the ASA Postulate to prove triangles congruentUse the ASA Postulate to prove triangles congruent Use.

Developing a Triangle Proof. 1. Developing Proof Is it possible to prove the triangles are congruent? If so, state the theorem you would use. Explain.

4.4 Proving Triangles are Congruent: ASA and AAS

WARM-UP. SECTION 4.3 TRIANGLE CONGRUENCE BY ASA AND AAS.

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

Prove Triangles Congruent by ASA & AAS

Proving Triangles Congruent Advanced Geometry Triangle Congruence Lesson 2.

4.4: Prove Triangles Congruent by ASA and AAS

Chapter 4.5 Notes: Prove Triangles Congruent by ASA and AAS Goal: You will use two more methods to prove congruences.

4.5 – Prove Triangles Congruent by ASA and AAS

4.3 & 4.4 Proving Triangles are Congruent

Chapter 4 Congruent Triangles.

SECTION 4.4 MORE WAYS TO PROVE TRIANGLES CONGRUENT.

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

EXAMPLE 1 Identify congruent triangles

(4.2)/(4.3) Triangle Congruence by SSS, SAS, ASA, or AAS Learning Target: To be able to prove triangle congruency by SSS, SAS, ASA, or AAS using proofs.

4.3 Triangle Congruence by ASA and AAS You can prove that two triangles are congruent without having to show that all corresponding parts are congruent.

Other methods of Proving Triangles Congruent (AAS), (HL)

9-5 Proving Triangles Congruent by Angle-Angle-Side (AAS) C. N. Colon St. Barnabas HS Geometry HP.

EXAMPLE 1 Identify congruent triangles Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem.

Warm-Up x + 2 3x - 6 What is the value of x?. Geometry 3-3 Proving Lines Parallel.

Warm Up Week 4 Describe what each acronym means: 1) AAA2) AAS 3) SSA4) ASA.

CHAPTER 4 Congruent Triangles. What does CONGRUENCE mean? Congruent angles- have equal measures Congruent segments- have equal lengths.

4.1 – 4.3 Triangle Congruency Geometry.

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.

For 9 th /10 th grade Geometry students Use clicker to answer questions.

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.

4.3 TRIANGLE CONGRUENCE BY ASA AND AAS TO PROVE TRIANGLE CONGRUENCE BY ASA POSTULATE AND AAS THEOREM.

4.10 Prove Triangles Cong. by ASA and AAS Angle-Side-Angle (ASA) Congruence Postulate If two angles and the included side of one triangle are congruent.

Geometry Sections 4.3 & 4.4 SSS / SAS / ASA

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

4.4 Proving Triangles are Congruent: ASA and AAS Geometry.

ASA AND AAS CONGRUENCE Section 4.5. Angle-Side-Angle (ASA) Congruence Postulate  If two angles and the included side of one triangle are congruent to.

Bell Work 12/12 State which two triangles, if any, are congruent, and write a congruence statement and reason why 1) 2) Solve for the variables 3) 4)

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.

Section 4-3 Proving Triangles Congruent by ASA and AAS.

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

Warm Up 5.3 on desk Do the Daily Quiz 5.2

Prove triangles congruent by ASA and AAS

Section 4-5 Triangle Congruence AAS, and HL

4.4 Proving Triangles are Congruent: ASA and AAS

Warm Up m<L = m<L = 180 m<L =

4.6: Triangle congruence ASA, AAS, & HL.

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?

5.3 Proving Triangles are congruent:

Other Methods of Proving Triangles Congruent

Three ways to prove triangles congruent.

4.3 and 4.4 Proving Δs are  : SSS and SAS AAS and ASA

Prove Triangles Congruent by ASA & AAS

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

4.4 Proving Triangles are Congruent: ASA and AAS

7-3 Similar Triangles.

Identifying types and proofs using theorems

Objective: To use a transversal in proving lines parallel.

4.5 Proving Δs are  : ASA and AAS

Proving Triangles are Congruent: ASA and AAS

Learn to use the ASA and AAS tests for congruence.

Triangle Congruence by ASA and AAS

(AAS) Angle-Angle-Side Congruence Theorem

4.4 Prove Triangles Congruent by SAS and HL

4.5 Proving Triangles are Congruent: ASA and AAS

Warm Up 1 ( Write a congruence statement

4-4/4-5 Proving Triangles Congruent

DRILL Statements Reasons

Presentation transcript:

GEOMETRY Proving Triangles are Congruent: ASA and AAS

Angle-Side-Angle (ASA) Congruence Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent.

Angle-Angle-Side (AAS) Congruence Theorem If two angles and a non- included side of one triangle are congruent to two angles and the corresponding non- included side of a second triangle, then the triangles are congruent.

Ex. 1 Developing Proof Is it possible to prove the triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning.

Ex. 1 Developing Proof Is it possible to prove the triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning.

Ex. 1 Developing Proof UZ ║WX AND UW ║WX. Is it possible to prove the triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning U W Z X

Ex. 2 Proving Triangles are Congruent Given: AD ║EC, BD  BC Prove: ∆ABD  ∆EBC Plan for proof: Notice that  ABD and  EBC are congruent. You are given that BD  BC Use the fact that AD ║EC to identify a pair of congruent angles.

Proof: Statements: 1. BD  BC 2. AD ║ EC 3.  D   C 4.  ABD   EBC 5. ∆ABD  ∆EBC Reasons: 1. Given 2. Given 3. Alternate Interior Angles 4. Vertical Angles Theorem 5. ASA Congruence Theorem

Note: You can often use more than one method to prove a statement. In Example 2, you can use the parallel segments to show that  D   C and  A   E. Then you can use the AAS Congruence Theorem to prove that the triangles are congruent.