CCSS ARGUMENTS Determine whether each statement is true or false. If false, give a counterexample. If true, explain your reasoning.
Two triangles with two pairs of congruent corresponding angles and three pairs of congruent corresponding sides are congruent.

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Two triangles with two pairs of congruent corresponding angles and three pairs of congruent corresponding sides are congruent: Always TRUE

What exactly does the term "triangle congruency" mean?

  • Two triangles are said to be congruent if their three corresponding sides are equal and their three corresponding angles are equal in size.
  • These triangles can be moved, rotated, flipped, and turned to appear identical.
  • If they are repositioned, they will coincide.
  • Two triangles are congruent if they satisfy all five congruence conditions.
  • They are the side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side  (RHS).

The statement states that:

  • Two triangles with two pairs of congruent corresponding angles and three pairs of congruent corresponding sides are congruent.
  • So, the statement is always true as it satisfies two conditions of congruency which are the SSS condition and AA condition.

Therefore, the statement "two triangles with two pairs of congruent corresponding angles and three pairs of congruent corresponding sides are congruent" is Always TRUE.

Know more about the congruency of a triangle here:

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