Chapter 4.3, Problem 4CYP

To determine

To Find: The two column proof for the given figure.

Answer to Problem 4CYP

The two column proof is shown in Table 1

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

The given data is, $\angle J\cong \angle P$ , $\overline{JK}\cong \overline{PM}$ , $\overline{JL}\cong \overline{PL}$ and $L$ bisects at $\overline{KM}$ .

The objective is to prove $\Delta JLK\cong \Delta PLM$ .

Calculation:

The objective is to prove $\Delta JLK\cong \Delta PLM$ .

The two column proof is shown in Table1

Table 1

$\angle J\cong \angle P$	Given
$\overline{JK}\cong \overline{PM}$, $\overline{JL}\cong \overline{PL}$	Given
$L$ bisects at $\overline{KM}$	Given
$\overline{KL}\cong \overline{LM}$	$L$ bisects at $\overline{KM}$
$\angle JLK\cong \angle MLP$	Opposite sides are equal
$\angle K\cong \angle M$	Angle sum property of the triangle