Question

Pls answer this!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! asap

Answer 1

Refer to the attached diagram for further a visual explanation. As per the given information, segments (AB) and (AD) are congruent. Moreover, segments (AC) and (AE) are also congreunt. One is also given that angles (<BAD) and (<EAC) are congruent. However, in order to prove the triangles (ABC) and (ADE) are congruent (using side-angle-side) congruence theorem, one needs to show that angles (<BAC) and (<DAE) are congruent. An easy way to do so is to write out angles (<BAC) and (<DAE) as the sum of two smaller angles:

<BAC = <BAD + <DAC

<DAE = <DAC + <EAC

Both angles share angle (DAC) in common, since angles (<EAC) and (BAD) are congruent, angles (<BAC) and (<DAE) must also be congruent.

Therefore triangles (ABC) and (ADE) are congruent by side-angle-side, thus sides (BC) and (DE) must also be congruent.

In summary:

AB = AD                                               Given

AC = AE                                               Given

<BAD = <EAC                                      Given

<DAC = <DAC                                     Reflexive

<BAC = <BAD + <DAC                       Parts-Whole Postulate

<DAE = <EAC + < DAC                       Parts-Whole Postulate

<BAC = <DAE                                      Transitivity

ABC = ADE                                          Side-Angle-Side

BC = DE                                               Corresponding parts of congruent triangles are congruent