Geometry/Properties

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[edit] Triangle Properties

The following triangles are congruent:

Side-Side-Side (SSS) (Postulate 12) If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

Side-Angle-Side (SAS) (Postulate 13)

If two sides and the included angle of a second triangle, then the two triangles are congruent.

Statements	Reasons
1)JL is congruent to NL	1) Given
2)L is midpoint of KM	2) Given
3)Angle JKL is congruent to angle NLM	3) Vertical angle theorem
4) Definition of midpoint	4)KL is congruent to ML
5) SAS Postulate	5)Triangle JKL is congruent to triangle NML

Angle-Side-Side (ASS)

The "ASS" postulate does not work, unlike the other ones. A way that students can remember this is that "ass" is not a nice word, so we don't use it in geometry (since it does not work).

Angle-Side-Angle

If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then two triangles are congruent.

Angle-Angle-Side

If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.