Chapter 4, Problem 14CT

To determine

To find: the method for the given two triangles being congruent.

Answer to Problem 14CT

The above two triangles are congruent by SAS postulate.

Explanation of Solution

Given information:

Given figure,

  

Calculation:

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

AAS Theorem: If two angles and non included side of a triangle is congruent to the corresponding parts of another triangle, then the triangles are said to be congruent.

HL Theorem: If the hypotenuse and a leg of one right triangle is congruent to the corresponding parts of another right triangle, then the triangles are said to be congruent

  

First name the figure accordingly.

In above figure consider $\Delta EFG$ and $\Delta ECD$

 1. $\overline{ED}\cong \overline{EG}$

Reason: Given

 2. $\overline{DF}\cong \overline{GC}$

Reason: given

 3. $\overline{ED}+\overline{EG}+\overline{EG}+\overline{GC}$

Reason: Add (1) & (2)

 4. $\overline{EF}\cong \overline{EC}$

Reason: Segment addition postulate

 5. $\angle E\cong \angle E$

Reason: Reflexive property

 6.Therefore, $\Delta EFG\cong \Delta ECD$

Yes, the above two triangles are congruent by SAS postulate.