Geometry section 4 4 cont aas
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Geometry Section 4.4 cont. AAS PowerPoint PPT Presentation


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Geometry Section 4.4 cont. AAS. In the last section we learned of three triangle congruence postulates :. SSS SAS ASA. We also saw why SSA does not work as a congruence “shortcut”. Let’s look at some other possibilities.

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Geometry Section 4.4 cont. AAS

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Geometry section 4 4 cont aas

Geometry Section 4.4 cont.AAS


In the last section we learned of three triangle congruence postulates

In the last section we learned of three triangle congruence postulates:

SSS SAS ASA


We also saw why ssa does not work as a congruence shortcut let s look at some other possibilities

We also saw why SSA does not work as a congruence “shortcut”.Let’s look at some other possibilities.


Geometry section 4 4 cont aas

A counterexample demonstrates that AAA is not a valid test for congruence. Consider two equiangular triangles. What is true about the angles in each triangle? Are the triangles shown congruent?

They are all 60 degrees.

No


Geometry section 4 4 cont aas

If we know the measures of two angles in a triangle, we will always be able to find the measure of the third angle.So, any time we have the AAS combination, we can change it into the ASA combination and the two triangles will then be congruent.


Geometry section 4 4 cont aas

Theorem 4.5 AAS (Angle-Angle-Side) Congruence TheoremIf two angles and the non-included side of one triangle are congruent to the corresponding parts of anothertriangle, then the triangles are congruent.


Geometry section 4 4 cont aas

Note: While ASA can be used anytime AAS can be used and vice-versa, they are different. The congruence markings on your triangles and the steps in your proof must agree with the congruence postulate/theorem you use.


Example are the triangles congruent and if so why

Example: Are the triangles congruent, and if so, why?


Geometry section 4 4 cont aas

Example 3: Name the congruent triangles and give the reason for their congruence. None is a possible answer.


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