Question

given the following congruent triangles write the 6 pairs of congruent corresponding parts. (3 pairs of congruent angles and 3 pairs of congruent sides)

Explanation:

Step1: Identify Congruent Sides

First, look at the markings on the sides. Side \( HG \) in \( \triangle FHG \) and side \( RT \) in \( \triangle RST \) have two tick marks, so \( HG \cong RT \). Then, we need to match the other sides based on the angle markings. The angles at \( H \) and \( T \) have two arc marks, and angles at \( G \) and \( R \) have one arc mark. So, side \( HF \) (opposite angle \( G \)) should correspond to side \( TS \) (opposite angle \( R \)), and side \( FG \) (opposite angle \( H \)) should correspond to side \( RS \) (opposite angle \( T \)). So \( HF \cong TS \) and \( FG \cong RS \).

Step2: Identify Congruent Angles

Angles with the same number of arc marks are congruent. Angle \( H \) (two arcs) and angle \( T \) (two arcs) are congruent: \( \angle H \cong \angle T \). Angle \( G \) (one arc) and angle \( R \) (one arc) are congruent: \( \angle G \cong \angle R \). The remaining angles, \( \angle F \) and \( \angle S \), should be congruent because the triangles are congruent, so \( \angle F \cong \angle S \).

Answer:

• Congruent Sides: \( HG \cong RT \), \( HF \cong TS \), \( FG \cong RS \)
• Congruent Angles: \( \angle H \cong \angle T \), \( \angle G \cong \angle R \), \( \angle F \cong \angle S \)