Question

9 multiple choice 2 points in the figure, ( m angle c n a=m angle w a n ) and ( c n=w a ). what congruence statement proves ( \triangle c a n cong \triangle w n a ) ? 10 multiple choice 2 points which is a right angle?

Explanation:

Step1: Analyze the congruence of triangles

For \(\triangle CAN\) and \(\triangle WNA\), we know \(CN = WA\) (given), \(\angle CNA=\angle WAN\) (given), and \(NA = NA\) (common side).

Step2: Apply the congruence criterion

By the Side - Angle - Side (SAS) congruence criterion, if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent. Here, in \(\triangle CAN\) and \(\triangle WNA\), \(CN = WA\), \(\angle CNA=\angle WAN\), \(NA = NA\).

Step3: Analyze the angles for the right - angle question

For \(\angle KJG\), \(\angle KJH+\angle HJG = 45^{\circ}+45^{\circ}=90^{\circ}\)

Answer:

1. A. SAS
2. C. \(\angle KJG\)