Triangle Congruence by SSS and SAS – How To Prove Triangles Congruent

Side Side Side Postulate

If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Example 1

Proving Triamgles Congruent with SSSThe first example is proving two triangles congruent using the SSS postulate. You are given two pairs of corresponding sides congruent. Thus, you need to only prove one pair of corresponding sides is congruent. As you can see in the diagram, the two triangles share a side segment BD. You will be able to establish this side is congruent to itself with the reflexive property of congruent segments. Now that all three sides are congruent, the triangles are congruent by the SSS postulate.

Example 2

Proving Triagles Congruent with SSSGiven that segment AX is congruent to segment AY and M is the midpoint of segment XY, Prove that triangle AMX is congruent to triangle AMY. First one can establish that segment AM is congruent to itself by the reflective property of congruence. That gives two pairs of corresponding sides of each triangle congruent. The third pair of corresponding sides, MX and MY, is congruent, because M is the midpoint of segment XY which is made up the segments MX and MY. Since all three pairs of corresponding sides are congruent, the triangles, AMX and AMY are congruent by SSS.

SAS Postulate

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

Example 3 Using SAS

This is actually example 2 in the video, but it is example 3 in the blog! Given that segment RS is congruent to segment TK.

What other information is needed to prove triangle RSK is congruent to triangle TKS By Side-Angle-Side?

Using Sid-Angle-Side

Since the triangles share side KS, it can be stated that segment KS is congruent to itself by the reflexive property of congruence. You now have two pairs of corresponding sides congruent. To prove the triangles congruent by SAS, angle RSK must be proved congruent to angle TKS.

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2 Responses

  1. […] a two column proof written in sentence form. In I have written many 10th grade geometric proofs on Side-Angle-Side and  Side-Side-Side. The above algebraic paragraph proof would look […]

  2. wow thanks, , ,that was helpful, , ,

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