Chapter 4, Problem 16MCQ

To determine

To explain:

Method which can be used to prove that $△\mathrm{A}\mathrm{B}\mathrm{D}\cong △\mathrm{C}\mathrm{B}\mathrm{D}$

Answer to Problem 16MCQ

Method which can be used to prove that $△\mathrm{A}\mathrm{B}\mathrm{D}\cong △\mathrm{C}\mathrm{B}\mathrm{D}$ is SAS (side angle side) congruent theorem.

Explanation of Solution

Given information:

  

It is given that $\overline{\mathrm{A}\mathrm{C}}\perp \overline{\mathrm{B}\mathrm{D}}$ and $\mathrm{B}$ is midpoint of $\overline{\mathrm{A}\mathrm{C}}$ .

A bisector cuts the segment into two parts.

  $\mathrm{B}\mathrm{D}\perp \mathrm{A}\mathrm{C}$

So, $△\mathrm{A}\mathrm{B}\mathrm{D}$ and $△\mathrm{B}\mathrm{D}\mathrm{C}$ are right angle triangle.

  $\angle \mathrm{A}\mathrm{B}\mathrm{D}\cong \angle \mathrm{B}\mathrm{D}\mathrm{C}$ as all right angle are $\cong$

  $\mathrm{B}\mathrm{D}\cong \mathrm{B}\mathrm{D}$ side.

Thus, by the (SAS) side angle side method it is prove that $△\mathrm{A}\mathrm{B}\mathrm{D}\cong △\mathrm{C}\mathrm{B}\mathrm{D}$ .