Given: ABCD is a rectangle
Prove triangle DAB is congruent to triangle CBA
**the rectangle is set up with D in the top left, C in the top right, A in the bottom left, B in the bottom right, and E in the middle of the intersecting lines
answers ??
To prove that triangle DAB is congruent to triangle CBA, we can use the criteria of congruence known as Side-Angle-Side (SAS).
Here's how we can prove it step by step:
Step 1: Given that ABCD is a rectangle, we know that opposite sides of a rectangle are congruent and all angles are right angles.
Step 2: Since ABCD is a rectangle, AD is parallel to BC, and AB is parallel to DC.
Step 3: Triangles DAB and CBA share the common side AB.
Step 4: Additionally, AD is congruent to BC since they are opposite sides of a rectangle, and DC is congruent to AB since they are also opposite sides of a rectangle.
Step 5: Therefore, we have side AB congruent to itself, side AD congruent to side BC, and side DC congruent to side AB.
Step 6: Since we have side AD congruent to side BC, side AB congruent to side AB, and side DC congruent to side AB, we have satisfied the SAS criteria of congruence.
Step 7: Therefore, triangle DAB is congruent to triangle CBA by SAS.
Overall, we used the properties of a rectangle (opposite sides are congruent and all angles are right angles) to establish the congruence between the corresponding sides of the triangles.