(C) 8. Developing Proof A balalaika is a stringed instrument. Prove that the bases of the balalaikas are congruent. Given: $$ \overline{R A} \cong \overline{N Y}, \angle K R A \cong \angle J N Y, \angle K A R \cong \angle J Y N $$ Prove: $$ \overline{K A} \cong \overline{J Y} $$ Proof: It is given that two angles and the included side of one triangle are congruent to two angles and the included side of the other. So, a. ? $$ \cong riangle J N Y $$ by b. .?. $$ \overline{K A} \cong \overline{J Y} $$ because c. ?.

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(C) 8. Developing Proof A balalaika is a stringed instrument. Prove that the bases of the balalaikas are congruent. Given: $$ \overline{R A} \cong \overline{N Y}, \angle K R A \cong \angle J N Y, \angle K A R \cong \angle J Y N $$ Prove: $$ \overline{K A} \cong \overline{J Y} $$ Proof: It is given that two angles and the included side of one triangle are congruent to two angles and the included side of the other. So, a. ? $$ \cong 	riangle J N Y $$ by b. .?. $$ \overline{K A} \cong \overline{J Y} $$ because c. ?.

UpStudy AI · Accepted Answer

1. From the given information, we know that  
   $$
   \overline{R A} \cong \overline{N Y},\quad \angle K R A \cong \angle J N Y,\quad \text{and} \quad \angle K A R \cong \angle J Y N.
   $$
2. In $$\triangle KRA$$ and $$\triangle JNY$$, the side $$\overline{RA}$$ is included between the two given angles. This satisfies the Angle-Side-Angle (ASA) condition.

3. Therefore,  
   $$
   \triangle KRA \cong \triangle JNY \quad \text{(by ASA)}.
   $$
4. By CPCTC (Corresponding Parts of Congruent Triangles are Congruent), we conclude that  
   $$
   \overline{KA} \cong \overline{JY}.
   $$
$$ \triangle KRA \cong \triangle JNY $$ by ASA, so $$ \overline{KA} \cong \overline{JY} $$.

© 8. Developing Proof A balalaika is a stringed instrument. Prove
that the bases of the balalaikas are congruent.
Given:
Prove:
Proof: It is given that two angles and the included side of one
triangle are congruent to two angles and the included side of the
other. So, a. ? by b. .?. because c. ?.

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© 8. Developing Proof A balalaika is a stringed instrument. Prove that the bases of the balalaikas are congruent. Given: Prove: Proof: It is given that two angles and the included side of one triangle are congruent to two angles and the included side of the other. So, a. ? by b. .?. because c. ?.