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Proving Congruent Triangles

Proving Congruent Triangles 1.4 - Solution

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Two triangles are congruent if their corresponding parts are congruent. We need to check whether corresponding sides and angles are congruent.

Are the Sides Congruent?

From the diagram, we can see that and Moreover, since any segment is congruent to itself. Therefore, the three sides of are congruent to the three sides of

Are the Angles Congruent?

To determine whether the third angles are congruent, we will first use the Triangle Angle Sum Theorem and the Transitive Property of Equality. In the given diagram, we see that and that Therefore, and Let's use this information to show that
Since we conclude that


Since all the corresponding parts are congruent, we can conclude that