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ASA
Five Shorts Cut For Determining If
Triangles Are Congruent
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If three sides of one triangle are congruent to three sides of another
triangle, then the two triangles are congruent by the SIDE-SIDE-SIDE
(SSS) Postulate.
If two sides and the included angle of one triangle are congruent to two
angles and the included of anther triangle, then the two triangles are
congruent by the SIDE-ANGLE-SIDE (SAS) Postulate.
If two angles and the included side of one triangle are congruent to two
angles and the included side of another triangle, then the two triangles
are congruent by the ANGLE-SIDE-ANGLE (ASA) Postulate.
If two angles and a non-included side of one triangle are congruent to
two angles and the corresponding nonincluded side of
another triangle, then the two triangles are congruent by the ANGLEANGLE-SIDE (AAS) Theorem.
If the hypotenuse and a leg of one right triangle are congruent to the
hypotenuse and a leg of another right triangle, then the triangles are
congruent.
Congruent Polygons
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What is Congruency- Congruency is polygons that have corresponding
sides congruent and corresponding angles congruent.
What does it mean for polygons to be congruent? If you have shown that
two polygons congruent then you know that every property of the
polygons is also identical. For example they will have the same area,
perimeter, exterior angles, apothern etc.
Triangle DEF is congruent to Triangle GHI
Angle-Side-Angle
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The angle side angle postulate 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 congruent.
The included side means the side between two angles. In
other words it is the side included between two angles.
Side Side Side Postulate
Proving Congruent Triangles
The Side Side Side postulate states that if
three sides of one triangle are congruent
to three sides of another triangle, then
these two triangles are congruent.