Geometry Sections 4.3 & 4.4 SSS / SAS / ASA.
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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.
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.
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.
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.
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.
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.
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.