Question

determine whether δi and δii are congruent. if the triangles are congruent, state the reason why, selecting from sss, sas, and asa. (more than one reason may be possible.)
select all that apply
□ asa
□ sss
□ sas
□ the triangles are not congruent.
□ there is not enough information to prove that the triangles are congruent or the triangles are not congruent

Explanation:

Step1: Identify shared sides/angles

The two triangles share a common side (the diagonal). Marked sides: two pairs of corresponding sides are equal (red ticks). Marked angles: one pair of corresponding angles is equal (red arcs).

Step2: Check congruence criteria

SAS requires two sides and included angle equal. Here, the equal angle is between the two equal sides and the common side? No—wait, the common side is adjacent to the equal angle, and the other two equal sides are opposite? Correction: Wait, the two triangles have two pairs of equal sides (marked) and the included angle? No, actually, the common side is one side, then two equal sides and the angle between the common side and one equal side? Wait no—standard SAS: if two sides and the included angle are equal. Since the common side is shared, two other sides are equal, and the angle between each equal side and the common side is equal (marked angle). So SAS applies.

Step3: Verify other criteria

SSS needs three sides equal—only two sides marked equal plus common side (three total), so SSS also applies? Wait, yes: common side is equal, two other sides equal → three sides equal (SSS). ASA needs two angles and included side—only one angle marked, so no.

Answer:

SSS, SAS