Question

question 11
triangle abc and triangle def are shown on the coordinate plane.
image of coordinate plane with triangles abc and def
which statement correctly names the congruent triangles and justifies the reason for congruence?

• △abc ≅ △fde by hl.
• △abc ≅ △fed by sas (selected).
• △abc ≅ △def by hl.
• △abc ≅ △def by sas.

Explanation:

Step1: Analyze Triangle Sides/Angles

Check sides (e.g., \( AC = DF = 3.2 \), \( AB = EF \) length) and angles (\( \angle A = \angle F = 72^\circ \)).

Step2: Identify Congruence Criterion

SAS (Side-Angle-Side) requires two sides and included angle. \( \triangle ABC \) and \( \triangle FED \) have \( AC = DF \), \( \angle A = \angle F \), \( AB = EF \) (included angle), so SAS applies. Other options (HL, incorrect triangle names) don't match.

Answer:

\( \triangle ABC \cong \triangle FED \) by SAS (the option with " \( \triangle ABC \cong \triangle FED \) by SAS ")