Question

a balalaika is a stringed instrument. prove that the bases of the balalaikas are congruent by filling in the blanks.
given: ( overline{ra} cong overline{ny}, angle r cong angle n, angle a cong angle y )
prove: ( overline{ka} cong overline{jy} )

Explanation:

Step1: Recall the ASA (Angle - Side - Angle) Congruence Postulate

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
In \(\triangle KRA\) and \(\triangle JNY\), we have \(\angle R\cong\angle N\), \(RA\cong NY\), and \(\angle A\cong\angle Y\). The side \(RA\) is included between \(\angle R\) and \(\angle A\) in \(\triangle KRA\), and the side \(NY\) is included between \(\angle N\) and \(\angle Y\) in \(\triangle JNY\).

Answer:

1. ASA (Angle - Side - Angle) Congruence Postulate