Chapter 4.7, Problem 20WE

To determine

To prove: $\overline{LX}\cong \overline{RY}$ .

Explanation of Solution

Given:

The given figure is,

  

And the condition is,

  $LX\text{and}RY$ are altitudes and $\Delta LMN\cong \Delta RST$ .

Statement :	Reason:
$\Delta LMN\cong \Delta RST$	Given
$\angle LMN\cong \angle RST$	Corresponding parts of congruent triangle
$\angle LMX\cong \angle RSY$	Corresponding parts of congruent triangle
$\angle LXM=\angle RYS=90°$	By SAS postulate
$\angle LMX\cong \angle RSY$	Corresponding parts of congruent triangle
$\Delta LXM\cong \Delta RYS$	By AAS postulate
$\overline{LM}\cong \overline{RS}$	Corresponding parts of congruent triangle