Unformatted text preview: Triangle Congruence Conditions: S A S , A S A , A A S , S S S , and (for right triangles) H L For a given correspondence of the vertices of two triangles, the Triangle Congruence Conditions
result from the fact that, for three particular parts of the triangles ( Ex: S-A-S, A-S-A, A-A-S, S-S-S ) if each of those three particular parts of one triangle is congruent to the corresponding part of the other
triangle, then, one can conclude immediately that the correspondence of vertices is a congruence
between the two triangles,
and thus, each side of one triangle is congruent to the corresponding side in the other triangle
and each angle of one triangle is congruent to the corresponding angle in the other triangle. If the two triangles are both right triangles with the right angles and hypotenuses corresponding,
then the congruence of the corresponding hypotenuses and the congruence of one pair of
corresponding legs ( H-L ) implies that the correspondence is a congruence between the
two right triangles. S A S (Side-Angle-Side) s s s (Side-Side-Side)
3 3' B 3'
1Q + Q a: + a: A c A' c' A c N c'
:>AABC E AA'B’C' =AABC E AA'B'C' A S A ( Angle-Si de- Angle) H L (Hypotenuse—Leg for right triangles only) 8 B' B B'
A + A A + k
A c A’ C' A c A. c- :AABC E AA'B'C' :AABC s AA'B'C' A A S (Angle-Angle—Side) => AABC _ AA'B’C' ll Note: There is no S-S-A Congruence Condition. Also, when applying the A-A-S Congruence Condition, you must be certain that the congruent
sides are opposite corresponding congruent angles. Here, it looks like A-A-S applies, but the triangles B B_ are not congruent. If you look closely, you see that 4 the the congruent sides are not opposite 4 55° 27-
corresponding congruent angles. 55° 27. A- c- ...
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- Spring '10