Chapter 4.6, Problem 4WE

To determine

To prove: $\overline{AL}\cong \overline{CM}$ .

Explanation of Solution

Given Information:

Given figure,

  

Key steps of proof:

a. $\Delta ABD\cong \Delta CDB$

b. $\overline{AD}\cong \overline{CB};\angle 1\cong \angle 2$

c. $\Delta ADL\cong \Delta CBM$

d. $\overline{AL}\cong \overline{CM}$

Calculation:

The key steps of the proof are:

1. $\Delta RNX\cong \Delta LOY$

Since two sides and one angle of one triangle are equal to two sides and one angle of another triangle.

Therefore, by side angle side congruency.

It is concluded that, two triangles are congruent.

2. $\angle X\cong \angle Y$ (Corresponding parts of $\cong \Delta$ are $\cong$)
3. $\Delta NEX\cong \Delta OSY$ (ASA Postulate)
4. $\overline{AL}\cong \overline{CM}$ (Corresponding parts of $\cong \Delta$ are $\cong$)

Hence, it is concluded that $\overline{AL}\cong \overline{CM}$ .