Question

1. draw the angle bisector from angle t in triangle cat. mark congruences appropriately.

Explanation:

Step1: Recall the definition of an angle bisector

An angle bisector is a ray that divides an angle into two congruent angles.

Step2: Analyze the options

• The first option shows a perpendicular line (marked with a right - angle symbol) from \(T\) to \(CA\). This is an altitude (if it's perpendicular to \(CA\)) or a median (if it bisects \(CA\)), not an angle bisector.
• The second option has a ray from \(T\) that divides \(\angle T\) into two congruent angles (marked with the same arc symbol). This satisfies the definition of an angle bisector.
• The third option has marks on \(CA\) indicating that it is bisected (mid - point marks). This is a median (a line segment from a vertex to the mid - point of the opposite side), not an angle bisector.

Answer:

The second option (the one with the ray from \(T\) that divides \(\angle T\) into two congruent angles marked with the same arc symbol) is the correct drawing of the angle bisector from angle \(T\) in triangle \(CAT\).