Chapter 4.2, Problem 18WE

To determine

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

Explanation of Solution

Given information:

Given figure,

Given:

  $\overline{TM}\parallel \overline{RP};\overline{TM}\cong \overline{PR}$

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:

  $\overline{TM}\parallel \overline{RP};\overline{TM}\cong \overline{PR}$

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

Proof:

Statements	Reasons
1. $\overline{TM}\parallel \overline{RP}$	Given
2. $\angle ETM\cong \angle EPRand\angle TME\cong \angle ERP$	Alternate interior angles
3. $\overline{TM}\cong \overline{PR}$	Given
4. $\Delta TEM\cong \Delta PER$	ASA Postulate