Question

a balalaika is a stringed instrument. prove that the bases of the balalaikas are congruent by filling in the blanks. given: \\( \overline { r a } \cong \overline { n y } , \angle r \cong \angle n , \angle a \cong \angle y \\) prove: \\( \overline { k a } \cong \overline { j y } \\) statements reasons 1. \\( \overline { r a } \cong \overline { n y } , \angle r \cong \angle n , \angle a \cong \angle y \\) 1. given 2. \\( \delta k r a \cong \delta j n y \\) 2. asa postulate (step 1) 3. \\( \overline { k a } \cong \overline { j y } \\) 3.

Explanation:

Step1: Recall the property of congruent triangles

If two triangles are congruent, then their corresponding parts are congruent. This is known as the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) theorem.

Step2: Apply the theorem

Since \(\triangle KRA\cong\triangle JNY\) (from step 2), and \(\overline{KA}\) and \(\overline{JY}\) are corresponding sides of these congruent triangles.

Answer:

CPCTC (Corresponding Parts of Congruent Triangles are Congruent)