Question

which two triangles are congruent? complete the congruence statement.

(image of three triangles: triangle wxy with angle w marked, side xy marked; triangle dcb with angle c marked, side dc marked; triangle hij with angle h marked, side ij marked. below: δ ≅ δ )

Explanation:

Step1: Identify congruent triangle criteria

Look for triangles with equal angles (marked arcs) and equal sides (marked ticks).

• $\triangle WXY$: Angle at $W$ (two arcs), side $XY$ (one tick), angle at $X$ (one arc).
• $\triangle HIJ$: Angle at $H$ (two arcs), side $IJ$ (one tick), angle at $I$ (one arc).
• $\triangle DCB$: Angle at $C$ (two arcs), side $DC$ (two ticks), angle at $B$ (one arc).

Step2: Match congruent parts

$\triangle WXY$ and $\triangle HIJ$ have:

• Two - arc angle (equal), one - arc angle (equal), and one - tick side (equal). By ASA (Angle - Side - Angle) or AAS (Angle - Angle - Side), they are congruent.

Answer:

$\triangle WXY \cong \triangle HIJ$