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Geometry Sections 4.3 & 4.4 SSS / SAS / ASA PowerPoint Presentation
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Presentation Transcript
slide2

To show that two triangles are congruent using the definition of congruent polygons, as we did in the proof at the end of section 4.1, we need to show that all ____ pairs of corresponding parts are congruent. The postulates introduced below allow us to prove triangles congruent using only ____ pairs of corresponding parts.

slide3

Postulate 19: SSS (Side-Side-Side) Postulate If 3 sides of one triangle are congruent to 3 sides of a second triangle, then the triangles are congruent.

slide4

We need to consider the following definitions to help us understand the next two postulates.In a triangle, an angle is included by two sides, if the angle In a triangle, a side is included by two angles, if the side

is formed by the two sides.

is between the vertices of the two angles.

slide6

Postulate 20: SAS (Side-Angle-Side) PostulateIf two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.

slide7

Why does the angle have to be the included angle? Why can’t we have ASS? Well, other than the fact that it is a bad word, ASS doesn’t always work to give us congruent triangles. Consider the following counterexample.

slide8

Postulate 21: ASA (Angle-Side-Angle) PostulateIf 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.

slide9

Example 3: Determine whether each pair of triangles can be proven congruent by using the congruence postulates. If so, write a congruence statement and identify the postulate used. None is a possible answer.