How do you prove that triangles are congruent with proofs?

SSS (Side-Side-Side) The simplest way to prove that triangles are congruent is to prove that all three sides of the triangle are congruent. When all the sides of two triangles are congruent, the angles of those triangles must also be congruent. This method is called side-side-side, or SSS for short.

What are the 5 methods for proving triangles congruent?

There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.

  • SSS (side, side, side) SSS stands for “side, side, side” and means that we have two triangles with all three sides equal.
  • SAS (side, angle, side)
  • ASA (angle, side, angle)
  • AAS (angle, angle, side)
  • HL (hypotenuse, leg)

Which congruence theorem can be used to prove △ ABC ≅ △ def?

Thus, all corresponding parts of congruent triangles are also congruent. Then △ ABC ≅ △ PQR by Angle Side Angle (ASA) rule. Then △ ABC ≅ △ XYZ by Side Angle Side (SAS) rule. Then △ ABC ≅ △ DEF by Side Side Side (SSS) rule.

What theorems could be used to prove the following triangles congruent?

Explanation: The Angle-Side-Angle Theorem (ASA) states that if two angles and their included side are congruent to two angles and their included side to another triangle, then these two triangles are congruent.

Is AAA a congruence theorem?

Knowing only angle-angle-angle (AAA) does not work because it can produce similar but not congruent triangles. When you’re trying to determine if two triangles are congruent, there are 4 shortcuts that will work. Because there are 6 corresponding parts 3 angles and 3 sides, you don’t need to know all of them.

Can SSA prove triangles congruent?

Is SSA a Criterion for Congruence of Triangles? No, the SSA congruence rule is not a valid criterion that proves if two triangles are congruent to each other.

What is the HL theorem?

The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

Does SAA prove congruence?

Angle-Angle-Side (AAS or SAA) Congruence Theorem: If two angles and a non-included side in one triangle are congruent to two corresponding angles and a non-included side in another triangle, then the triangles are congruent.

How do you know if it’s AAS or ASA?

If two pairs of corresponding angles and the side between them are known to be congruent, the triangles are congruent. This shortcut is known as angle-side-angle (ASA). Another shortcut is angle-angle-side (AAS), where two pairs of angles and the non-included side are known to be congruent.

What is the AAA theorem?

Euclidean geometry may be reformulated as the AAA (angle-angle-angle) similarity theorem: two triangles have their corresponding angles equal if and only if their corresponding sides are proportional.