We are asked to prove that in the overlapping triangles shaded in the diagram are congruentrectangle ABCD. We will use the given figure to check the relationships between its sides and angles. We see that only one right angle is marked. However, we know that all angles of a rectangle are right angles! Let's mark two of these.
In relation to congruence, let's now summarize what we know about triangles △ ADC and △ BCD.
The angles of a rectangle are right angles and all right angles are congruent.
DC≅CD
It is a common side of the two triangles.
We can see that two sides and the included angle of triangle △ ADC is congruent to two sides and the included angle of triangle △ BCD. According to the Side-Angle-Side (SAS) Congruence Postulate, these two triangles are congruent.
△ ADC≅ △ BCD
To summarize the process of proving that these two triangles are congruent, we will use a two-column proof.
Completed Proof
2
&Given:&& ABCDis a rectangle
&Prove:&& △ ADC≅△ BCD
Proof:
