Congruent Triangles and different Congruency Criteria

Contributed by:

Diego Thu, Jan 27, 2022 12:26 PM UTC

This pdf contains:-
SSS (Side Side Side)
SAS (Side Angle Side)
ASA (Angle Side Angle)
AAS (Angle Angle Side)
RHS (Right angle Hypotenuse Side)

1. CONGRUENT TRIANGLES
2 Triangles are CONGRUENT if they have:
Corresponding SIDES congruent(same length)
Corresponding ANGLES congruent (same degree measure)
**We don’t have to know all 3 sides and all 3 angles…just
3 out of the 6 is enough**
Congruent polygons have the EXACT same size and shape.
They may slide, flip, or turn to fit exactly on top of the
other one.

2. There are 5 methods to prove triangles

3. SSS Postulate
The Side Side Side postulate (often abbreviated as SSS) states that if
three sides of one triangle are congruent to three sides of
another triangle, then these two triangles are congruent.

4. SAS Postulate
• The Side Angle Side postulate (often abbreviated as SAS) states that if
two sides and the included angle of one triangle are congruent to two
sides and the included angle of another triangle, then these
two triangles are congruent.
• EX:

5. ASA Postulate
• The Angle Side Angle postulate (often abbreviated as ASA) states that
if two angles and the included side of one triangle are congruent to
two angles and the included side of another triangle, then these
two triangles are congruent.
• EX:

6. AAS
• The AAS Theorem. The angle-angle-side Theorem, or AAS, tells us that if
two angles and any side of one triangle are congruent to two angles and
any side of another triangle, then the triangles are congruent.
• http://study.com/academy/lesson/the-aas-theorem.html
• EX:

7. HL Theorem
• And then there's the hypotenuse leg theorem, or HL theorem.
This theorem states that 'if the hypotenuse and one leg of a right
triangle are congruent to the hypotenuse and one leg of another right
triangle, then the triangle are congruent.’
• http://study.com/academy/lesson/the-hl-theorem.html
• EX:

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