High School

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Why are triangles congruent?

A. A triangle ABC is bisected by a vertical line AD to form two right-angle triangles, in which CD and BD are congruent, and AC and AB are congruent.

B. A triangle ABC is divided into three equal parts, making all sides congruent.

C. A triangle ABC has three angles that sum up to 180 degrees.

D. Triangles are not always congruent; congruence depends on their side lengths and angles.

Answer :

The answer is: d. Triangles are not always congruent; congruence depends on their side lengths and angles.

The statement "Triangles are not always congruent; congruence depends on their side lengths and angles" is correct. Congruence in triangles is determined by both their side lengths and angles. Triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in measure.

Option a refers to the bisection of a triangle, but this doesn't necessarily make the triangles congruent. Option b describes dividing a triangle into three equal parts, which doesn't guarantee congruence. Option c states a property of triangles but does not provide a condition for congruence.

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Rewritten by : Jeany