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.

Slides:

Advertisements

Similar presentations

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.

Advertisements

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

GEOMETRY Proving Triangles are Congruent: ASA and AAS.

4.4 Proving Triangles are Congruent: ASA and AAS

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

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

TODAY IN GEOMETRY…  Go over proofs from HW #5  4.4 WS Warm Up  Learning Goal: 4.5 You will use postulates Angle-Side-Angle and Angle-Angle-Side to prove.

Lesson 3-4 Proving lines parallel,. Postulates and Theorems Postulate 3-4 – If two lines in a plane are cut by a transversal so that corresponding angles.

(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.

Triangle Congruence by ASA and AAS Chapter 4 Section 3.

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.

Chapter 4: Triangle Congruence Missy McCarthy Okemos High School Math Instructor.

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.

4.6 Prove Triangles Congruent by ASA and AAS

Angle Relationship Proofs. Linear Pair Postulate  Angles which form linear pairs are supplementary.

EXAMPLE 3 Prove the Vertical Angles Congruence Theorem

Proving Lines Parallel

3-3 Proving Lines Parallel

4.3: Triangle Congruence by ASA and AAS 4.4: CPCTC If I'm not back in five minutes...just wait longer!" -Ace Ventura If I'm not back in five minutes...just.

4.7 ASA and AAS Objectives: Apply ASA and AAS to construct triangles and to solve problems. Prove triangles congruent by using ASA and AAS.

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.

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.

1 2 Parallel lines Corresponding angles postulate: If 2 parallel lines are cut by a transversal, then corresponding angles are congruent….(ie.

If I'm not back in five minutes...just wait longer!"

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.

Using Special Quadrilaterals

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.

Prove triangles congruent by ASA and AAS

Proving Triangles are Congruent

Corresponding Angles Postulate

Proving Lines are Parallel

5.3 Proving Triangles are congruent:

3.3 Proving Lines are Parallel

Warm Up (on the ChromeBook cart)

Chapter 3.2 Notes: Use Parallel Lines and Transversals

Prove Triangles Congruent by ASA & AAS

A proof that uses arrows to show

5.6 Proving Triangle Congruence by ASA & AAS

Class Greeting.

Warm Up (on handout).

Objective: To use a transversal in proving lines parallel.

3-2 Properties of Parallel Lines

Proving Triangles are Congruent: ASA and AAS

Parallel Lines and Transversals

Learn to use the ASA and AAS tests for congruence.

Parallel lines and Transversals

Prove Triangles Congruent by SAS

Triangle Congruence by ASA and AAS

Properties of parallel Lines

4.3 Triangle Congruence by ASA and AAS

Proving Statements about Angles

Unit 2: Congruence, Similarity, & Proofs

Parallel Lines and Transversals

4-4/4-5 Proving Triangles Congruent

3.2 Notes: Use Parallel Lines and Transversals

Presentation transcript:

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 to two angles and the included side of a second triangle, then the two triangles are congruent. A C B D E F

4.10 Prove Triangles Cong. by ASA and AAS Theorem 4.13: 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 two triangles are congruent. A C B D E F

4.10 Prove Triangles Cong. by ASA and AAS Theorem 4.14: Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then the pair of alternate interior angles are _________. congruent 4 5 p q t

4.10 Prove Triangles Cong. by ASA and AAS 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 you would use. a. a.There is not enough information to prove the triangles congruent, because no _______ are known to be the congruent. sides

4.10 Prove Triangles Cong. by ASA and AAS 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 you would use. b. b.Two pairs of angles and a ______________ pair of sides are congruent. The triangles are congruent by the _____________________________. non-included AAS Congruence Theorem

so two pairs of angles and their _______________ are congruent. The triangles are congruent by the ____________________________ Prove Triangles Cong. by ASA and AAS 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 you would use. c. c.The vertical angles are congruent, included sides ASA Congruence Postulate

4.10 Prove Triangles Cong. by ASA and AAS Checkpoint. Complete the following exercises. 1.Can STW and VWT be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use. S T U W V you have two pairs of angles and a non-included pair of sides. The triangles are congruent by the AAS Congruence Theorem

4.10 Prove Triangles Cong. by ASA and AAS Example 2 Write a flow proof In the diagram, 1 4 and CF bisects ACE. Write a flow proof to show CBF CDF. C E B A D F Given: Prove: Given Def. of _______________ angles supplements supplementary Cong. Supps. Thm. Reflexive Prop. _________________________ AAS Congruence Theorem

4.10 Prove Triangles Cong. by ASA and AAS Checkpoint. Complete the following exercises. C E B A D F In the diagram, CF bisects ACE and BFD. Write a flow proof to show CBF CDF. Given: Prove: Given Def. of bisector Reflexive Prop. ASA Congruence Postulate

4.10 Prove Triangles Cong. by ASA and AAS Pg. 267, 4.10 #1-20