ASA and SAS Triangle Congruence Theorems

Slides:

Advertisements

Similar presentations

4-4 Using Congruent Triangles: CPCTC

Advertisements

Hypotenuse – Leg Congruence Theorem: HL

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

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

Triangle Congruence by ASA and AAS Chapter 4 Section 3.

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

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.

Honors Geometry Section 4.3 cont. Using CPCTC. In order to use one of the 5 congruence postulates / theorems ( )we need to show that 3 parts of one triangle.

Triangle Congruence Theorems

Prove triangles congruent by ASA and AAS

Geometry-Part 7.

4-2 Triangle Congruence by SSS and SAS

5.2 Proving Triangles are Congruent by SSS and SAS

Proving Triangles are Congruent

7.4 Showing Triangles are Similar: SSS and SAS

5.1 Exploring What Makes Triangles Congruent

Proving Triangles Congruent

4.6: Triangle congruence ASA, AAS, & HL.

Similarity Postulates

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?

Triangle Congruence Theorems

Proving Triangles Congruent

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

4.4 Hypotenuse-Leg (HL) Congruence Theorem

Right Triangles What are the additional congruence theorems used only for right triangles? Which combination of sides for triangles in general cannot.

5.3 Proving Triangles are congruent:

Proving Triangles Congruent: SSS and SAS

4-2 Triangle Congruence by SSS and SAS

Other Methods of Proving Triangles Congruent

Proving Triangles Congruent

Three ways to prove triangles congruent.

4-3 Triangle Congruence by ASA and AAS

4-4 and 4-5: Congruent Triangle Theorems

Section 21.2: AAS Triangle Congruence

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

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

Proving Triangles Similar Related Topic

What if we enlarged the rectangle by a scale of 2:1, what is the area then? Rectangle C 2 cm 5 cm Example 2.

Triangle Congruence.

Triangle Congruence HL and AAS

Identifying types and proofs using theorems

SAS and AAS Triangle Congruence Theorems

Warm Up Draw a triangle with the following specifications

4.1 Congruent Figures -Congruent Polygons: have corresponding angles and sides -Theorem 4.1: If 2 angles of 1 triangle are congruent to 2 angles of another.

Proving Triangles Similar.

Triangle Congruence Theorems

Congruence and Triangles

Get out your Module 4 quiz and

Learn to use the ASA and AAS tests for congruence.

5.2 ASA Triangle Congruence

4-1 Congruent Figures 4-2 Triangle Congruence by SSS and SAS

Proving Triangles Similar.

Warmup Write a congruence statement for the triangles.

Triangle Congruence by ASA and AAS

(AAS) Angle-Angle-Side Congruence Theorem

Proving Triangles are Congruent

Triangle Congruency Theorems (shortcuts)

4.5 Proving Triangles are Congruent: ASA and AAS

Congruent Triangles.

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.

4-2 Triangle congruence by sss & sas

4-1 Congruent Figures 4-2 Triangle Congruence by SSS and SAS

4.2 /4.3 – Triangle Congruence

Presentation transcript:

ASA and SAS Triangle Congruence Theorems Dania Sandoval period 6

What does ASA and SAS stand for? ASA stands for: Angle Side SAS stands for: Side Angle

What is ASA? ASA means that we have two triangles where we know two sides corresponding sides and their included angle is congruent.

ASA Postulate If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

What is SAS? SAS means that we have two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent

SAS Postulate If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Why are these theorems important? Theorems are important because they help us identify the congruence two triangles can have using any of the triangle congruences postulates. These two help, and all we do is look at the sides and angles of a triangle. And it doesn’t just need to be in Geometry class, either. We can go around, comparing buildings using these two theorems.

How are these Theorems important? These theorems are important in real life. For example, if you want to be an architect, it is important for architectural designs in order to be able to tell if one building/ part of building is congruent to the other triangular shape you are making.

Real World Examples ASA SAS SAS ASA