Given: $\overset{炉}{B E}$ bisects $鈭� D B A; 鈭� 3 鈮� 鈭� 1$
Prove: $\overset{炉}{C D}|| \overset{炉}{B E}$

Short Answer

Expert verified

The conclusion represent that $\overset{炉}{C D} 鈥� \overset{炉}{B E}$ .

Step by step solution

Step 1. Determine the theorem or postulate that can be used

The theorem 3-5 can be used which states that the relation between two lines is parallel only when a separate line travels through these two lines and the angles which are positioned on the alternate interior side represents the congruent angles.

The definition of transitive property of congruence states that whenever two angles are congruent and if any one of them is congruent to another angle that is beside those two angles then the second angle from first two angles also congruent to the another angle. According

Step 2. Determine the congruent angles except the provided angles

According to the provided bisection of angle $m 鈭� D B E = m 鈭� E B A$ which means that $m 鈭� 2 = m 鈭� 3$ . As the measurements are equal so this will result in $鈭� 2 鈮� 鈭� 3$ .

By using the transitive property, $鈭� 2 鈮� 鈭� 3$ and provided angles the angle $鈭� 1 鈮� 鈭� 2$ .

Step 3. Make the conclusion

The angles $鈭� 1$ and $鈭� 2$ are associated with the lines $\overset{炉}{C D}$ and $\overset{炉}{B E}$ because a separate line role="math" localid="1637916925571" $\overset{炉}{D B}$ is travelling through these lines and result in formation of angles $鈭� 1$ and $鈭� 2$ . According to the theorem 3-5 the lines $\overset{炉}{C D}$ and $\overset{炉}{B E}$ are having a parallel connection between them.