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SSS, SAS, ASA, AAS, RHS. SSA can prove congruence if the angle in question is obtuse (if it's 90 degrees, then it's exactly equivalent to RHS).

Q: What are the five triangle congruency theorems?

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SAS (Side-Angle-Side) is a geometric term that describes if two triangles are congruent - whether it is a right triangle or not.

if any two angles are similar the triangle will be similar

If the hypotenuse and one leg of a right angled triangle are congruent to the hypotenuse and leg of another right angled triangle, then the two triangles are congruent.

... may be acute, right, or obtuse.

You will also need the angles so that you can use the Isosceles Triangle Theorems to solve for the base of isosceles triangle when only two sides are given.

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Incentre.

triangle congruency

Congruency can only be determined between two regular polygons.

Yes he is known for the theorem that has his name.

The two triangle congruence theorems are the AAS(Angle-Angle-Side) and HL(Hypotenuse-Leg) congruence theorems. The AAS congruence theorem states that if two angles and a nonincluded side in one triangle are congruent to two angles and a nonincluded side in another triangle, the two triangles are congruent. In the HL congruence theorem, if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, the two triangles are congruent.

SAS (Side-Angle-Side) is a geometric term that describes if two triangles are congruent - whether it is a right triangle or not.

You can find the angle of a triangle within a circle segment using the circle theorems.

if any two angles are similar the triangle will be similar

If the hypotenuse and one leg of a right angled triangle are congruent to the hypotenuse and leg of another right angled triangle, then the two triangles are congruent.

HA, LA, HL, LL [APEX]

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Pythagoras