Chapter 4.2, Problem 11CE

(a)

To determine

To list: two pairs of congruent corresponding sides and one pair of congruent corresponding angles in $\Delta YTR$ and $\Delta XTR$ .

Answer to Problem 11CE

The two pairs of congruent corresponding sides are,

  $\begin{array}{l}\overline{YT}\cong \overline{XT}\\ \text{and,}\\ \overline{TR}\cong \overline{TR}\end{array}$

And, one pair of congruent angles is

  $\angle R\cong \angle R$

Explanation of Solution

Given information:

Given figure,

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.

In $\Delta YTR$ & $\Delta XTR$ ,

The two pairs of congruent corresponding sides are,

  $\begin{array}{l}\overline{YT}\cong \overline{XT}\\ \text{and,}\\ \overline{TR}\cong \overline{TR}\end{array}$

And, one pair of congruent angles is

  $\angle R\cong \angle R$

(b)

To determine

Whether SSA rule is enough to guarantee that two triangles are congruent.

Answer to Problem 11CE

These triangles can never be congruent and SSA is not postulate.

Explanation of Solution

Given information:

Given figure,

In given triangle, two sides and a nonincluded angle.

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.

No, SSA is not enough to gurantee that two triangles are congruent. As, see in the above figure $\Delta XTR$ is a part of $\Delta YTR$ . Thus, these triangles can never be congruent and SSA is not postulate.