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## Proving Triangles Congruent Using Definition of Congruent Triangles

The second part of this series about congruent figures is proving triangles congruent. If you are interested in the reading the first post on Congruent Figures. At this point, there is only one way to prove triangles congruent, with the definition of congruent triangles. Congruent triangles have 3 pairs of corresponding angles and 3 pairs of congruent angles. So, to prove two triangles congruent, we must establish that all 3 pairs of corresponding sides and angles are congruent. The third angle theorem states, if two angles of one triangle are congruent to two angles of another triangle, the third angles are congruent to each other.

Given: segment AB is congruent to segment AD, segment BC is congruent to segment DC, angle B is congruent to angle D, and angle BAC is congruent angle DAC

Prove: triangle ABC is congruent to triangle ADC

Prove Triangle ABC congruent to Triangle ADC

With the given information: segment AB is congruent to segment AD, segment BC is congruent to segment DC, angle B is congruent to angle D, and angle BAC is congruent angle DAC, prove triangle ABC is congruent to triangle ADC. Segment AC is congruent to segment AC by the reflexive property of congruence. Next, it must be established that angle ACB is congruent to angle ACD, by the third angle theorem. Since, all three pairs of corresponding sides and angles are congruent, triangle ABC is congruent to triangle ADC.