4.4 Proving Triangles are Congruent: ASA and AAS Geometry.

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

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

Congruent Figures Congruent Polygons have congruent corresponding parts- their matching sides and angles.

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

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 Proving Triangles Congruent

GEOMETRY Proving Triangles are Congruent: ASA and AAS.

4.4 Proving Triangles are Congruent: ASA and AAS

WARM-UP. SECTION 4.3 TRIANGLE CONGRUENCE BY ASA AND 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

Proving Triangles Congruent. Two geometric figures with exactly the same size and shape. Review of Congruence A C B DE F.

4.3 & 4.4 Proving Triangles are Congruent

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

Proving Triangles Congruent Geometry Ch 04 A BowerPoint Presentation.

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

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

Geometry 4-5 ASA, AAS, and HL. Vocab. Word An included side is the common side of two consecutive angles in a polygon. (The side in between two angles)

Proving Triangles Congruent

(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.

Congruent Triangles have six sets of corresponding parts! Three sets of corresponding sides Three sets of corresponding angles.

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.

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

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

Triangle Congruency Classifying Triangles by Sides Equilateral Triangle 3 congruent sides Isosceles Triangle At least 2 congruent sides Scalene Triangle.

Math 2 Geometry Based on Elementary Geometry, 3 rd ed, by Alexander & Koeberlein 3.1 Congruent Triangles.

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

4.1 – 4.3 Triangle Congruency Geometry.

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.

Mr. Schaab’s Geometry Class Our Lady of Providence Jr.-Sr. High School

 If three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.  If AB = DE, BC = EF, AC.

Proving Triangles Congruent. How much do you need to know... need to know about two triangles to prove that they are congruent?

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

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

Are the following triangles congruent? Why or why not? Write a congruence statement for the triangles. 21 ° 74 ° 85 ° 21 ° 74 ° 85 ° T S R L M N.

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.

Holt McDougal Geometry 4-6 Triangle Congruence: ASA, AAS, and HL Angle Side Angle, Angle Angle Side Triangle Congruence.

Do Now: Identify two congruent triangles in the figure below. H N A D.

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

Do-Now 2) Find the value of x & the measure of each angle. 5x – 4 4x ° 1) Find the value of x. 4x x – 10 3x + 1 5x – 4 + 4x + 14 = 100 9x.

Side-side-side (SSS) postulate If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Review: Solving Systems x 2y+3 x+y 12 Find the values of x and y that make the following triangles congruent.

Prove triangles congruent by ASA and AAS

4.4 Proving Triangles are Congruent: ASA and AAS

Proving Triangles are Congruent

4.6: Triangle congruence ASA, AAS, & HL.

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

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?

Proving Triangles Congruent

Featuring ASA and AAS (angle-side-angle and angle-angle-side)

Proving Triangles Congruent

5.3 Proving Triangles are congruent:

Proving Triangles Congruent

Proving Triangles Congruent

4-3 Triangle Congruence by ASA and AAS

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

Identifying types and proofs using theorems

4.5 Proving Δs are  : ASA and AAS

4-5 Proving Congruence Included side: the side between the 2 angles used. AB is the included side between angles A and B. BC is the included side between.

Learn to use the ASA and AAS tests for congruence.

(AAS) Angle-Angle-Side Congruence Theorem

Warm Up 1 ( Write a congruence statement

4-4/4-5 Proving Triangles Congruent

Presentation transcript:

4.4 Proving Triangles are Congruent: ASA and AAS Geometry

Objectives: 1.Prove that triangles are congruent using the ASA Congruence Postulate and the AAS Congruence Theorem 2.Use congruence postulates and theorems in real-life problems.

Postulate 21: 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.

Theorem 6.1 If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent.

Theorem 4.5: 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.

Theorem 4.5: Angle-Angle-Side (AAS) Congruence Theorem Given:  A   D,  C   F, BC  EF Prove: ∆ABC  ∆DEF