Download 5 Ways To Show Triangle Congruence

5 Ways To Show Triangle Congruence
1. SAS = SAS Congruence Postulate - if two sides and the included
angle of one triangle are congruent to two sides and the included angle of
a second triangle, then the two triangles are congruent.
Example: Given ΔABC and ΔDEF, if AB = DE, BC = EF and angle B = angle
E, then ΔABC = ΔDEF.
2. SSS = SSS Congruence Postulate - if three sides of one triangle are
congruent to three sides of a second triangle, then the two triangles are
congruent.
Example: Given ΔABC and ΔDEF, if AB = DE, BC = EF and AC = DF, then
ΔABC = ΔDEF.
3. ASA = ASA Congruence Postulate - if two angles and the included
side of one triangle are congruent to two angles and the included side of a
second triangle, then the two triangles are congruent.
Example: Given ΔABC and ΔDEF, if angle A = angle D, AB = DE, and
angle B = angle E, then Δ ABC = Δ DEF.
4. AAS = AAS Congruence Postulate - if two angles and a nonincluded 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.
Example: Given Δ ABC and Δ DEF, if angle A = angle D, angle C = angle F,
and BC = EF, then Δ ABC = Δ DEF.
5. HL = HL Congruence Postulate - if the leg and hypotenuse of one
right triangle is congruent to the corresponding leg and hypotenuse of
another right triangle, then the two triangles are congruent by hypotenuse
- leg postulate.
Example: Given right Δ ABC and right Δ DEF, if angle B and angle E are
both right angles and leg AB = leg DE and hypotenuse AC = hypotenuse
DF, then Δ ABC = Δ DEF.