There are five ways to find two congruent triangles:
• SSS or Side Side Side
• SAS or Side Angle Side
• AAS or Angle Side
• HL or Hypotenuse Leg, right triangles only
Two triangles are congruent if corresponding side lengths are equal and corresponding interior angles are equal.
Side Side Side Postulate
Postulate is true without certification. The SSS postulate tells us that two triangles are congruent if three sides of the triangle are congruent with three sides of another triangle.
If the ACE has three sides that are identical to the three sides of the HUM, then by SSS the two triangles are congruent.
Side Angle Side postulate
This postulate states that two triangles are congruent if the two angles and the inscribed side of the triangle are congruent to the two angles and the inscribed side of another triangle. Two triangles are congruent if the side is an included angle of another triangle. The sides, included angles, and sides of HUG and LAB are congruent. Therefore, according to SAS, the two triangles are congruent.
Angle Angle Side postulate
Given two corners and a side that is not contained opposite one of the corners. The angle-angle-side theorem states that triangles are congruent if two angles and the non-inclusive side of the triangle are congruent with the corresponding parts of another triangle.
HL Postulate
For right triangles only, the HL postulate tells us that "two right triangles with congruent hypotenuses and corresponding congruent legs are congruent".
To learn more about congruence postulate, refer:
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