Chapter 4.2, Problem 19WE

To determine

To prove: $\Delta TEM\cong \Delta PER$ using two column form.

Explanation of Solution

Given information:

Given figure,

Given:

$E$ is the midpoint of $\overline{TP}$ ;

$E$ is the midpoint of $\overline{MR}$

Calculation:

SSS Postulate: if there sides of triangle are equal to the three corresponding sides of another triangle, then the triangles are congruent.

SAS Postulate: If two sides and the angle included between them of triangle are equal to the two corresponding sides and the angle included between them of another triangle, then the triangles are congruent.

ASA Postulate: If two angles and the included side of triangle are equal to the two corresponding angles and the included sides of another triangle, then the triangles are congruent.

Given:

$E$ is the midpoint of $\overline{TP}$ ;

$E$ is the midpoint of $\overline{MR}$

Prove: $\Delta TEM\cong \Delta PER$

Proof:

Statements	Reasons
1. $E$ is the midpoint of   $\overline{TP}$	Given
2. $\overline{TE}\cong \overline{PE}$	Definition of midpoint
3. $E$ is the midpoint of   $\overline{MR}$	Given
4. $\overline{ME}\cong \overline{RE}$	Definition of midpoint
5. $\angle TEM\cong \angle PER$	Vertically angles are congruent
6. $\Delta TEM\cong \Delta PER$	SAS postulate