Question

1. are the two triangles congruent? why or why not? if they are congruent, write a congruence statement.

Explanation:

Step1: Identify marked congruent parts

Triangle ART and triangle LOG have two pairs of congruent angles (∠A≅∠L, ∠T≅∠O) and one pair of congruent sides (side with single tick mark).

Step2: Apply congruence criterion

The congruent side is between the two congruent angles, so ASA (Angle-Side-Angle) applies.

Step3: Write congruence statement

Match corresponding vertices: A↔L, R↔G, T↔O.

Answer:

Yes, the triangles are congruent by ASA. The congruence statement is $\triangle ART \cong \triangle LOG$.