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 4 ways to prove triangles are 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 is Asa rule in maths?

The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

What is the condition of congruency?

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

How many congruency criterions are there name them?

Two triangles are congruent if they satisfy the 5 conditions of congruence. They are side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS) and right angle-hypotenuse-side (RHS).

What is missing reason in the proof?

the reason missing in the table of proof. Solution, Option (4) is the correct option. It is the converse alternate interior angles theorem that is missing from the given table. The theorem states that “If two lines are cut by a transversal so that the alternate interior angles are congruent, then the lines are parallel …

Which pair of triangles can be congruent by SAS?

Side-angle-side (SAS) When two pairs of corresponding sides and the corresponding angles between them are congruent, the triangles are congruent.

What does SSS stand for in math?

Two triangles are congruent if they have the same size and shape. Here are the four common ways to prove that two triangles are congruent: SSS (side-side-side) All three corresponding sides are congruent.