Chapter 4, Problem 6CR

To determine

To find: the postulate can be used for deduction of $\Delta RXY\cong \Delta SXY$ from the given information.

Answer to Problem 6CR

But no congruence can be deduced by SSS, SAS, AAS, ASA and HL postulate.

Explanation of Solution

Given information:

Given:

  $\overline{RY}\cong \overline{SY};\angle R\cong \angle S$

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.

  

Given: $\overline{RY}\cong \overline{SY};\angle R\cong \angle S$

Prove: $\Delta RXY\cong \Delta SXY$

Proof:

As see in above triangles:

 1. $\overline{RY}\cong \overline{SY}$

Reason: Given

 2. $\angle R\cong \angle S$

Reason: given

 3. $\overline{XY}\cong \overline{XZ}$

Reason: Reflexive property

But no congruence can be deduced by SSS, SAS, AAS, ASA and HL postulate.