Question

2 multiple choice 25 points state how the triangles are congruent. indique cómo los triángulos son congruentes. image of triangles with vertices a, c, e (left) and b, d, e (right), with congruency markings on sides and angles options: aaa, ass or ssa, aas or saa, hl, sas, asa

Explanation:

Step1: Analyze given triangle parts

From the diagram, we have vertical angles at \( E \), so \( \angle AEC=\angle BED \) (vertical angles are equal). We also have a marked side (congruent segments) and a marked angle (congruent angles) at \( C \) and \( B \) respectively. Wait, actually, let's re - examine: the triangles are \( \triangle AEC \) and \( \triangle BED \) (assuming the intersection is at \( E \)). We have \( \angle C=\angle B \) (marked angles), \( EC = EB \) (marked sides), and \( \angle AEC=\angle BED \) (vertical angles). So we have two angles and a side: angle - side - angle? Wait no, wait: \( \angle C \), \( EC \), \( \angle AEC \) for \( \triangle AEC \); \( \angle B \), \( EB \), \( \angle BED \) for \( \triangle BED \). Wait, actually, the correct congruence: we have two angles and a non - included side? No, wait, let's check the options. Wait, AAS (Angle - Angle - Side) or SAA: in AAS, two angles and a non - included side are congruent. Let's see: we have \( \angle C=\angle B \), \( \angle AEC=\angle BED \) (vertical angles), and \( AC \) and \( BD \)? No, wait the marked sides are \( EC \) and \( EB \). Wait, maybe I made a mistake. Wait, the triangles: let's consider the angles. \( \angle C=\angle B \) (given by the marks), \( \angle AEC=\angle BED \) (vertical angles), and the side \( EC = EB \) (marked). Wait, no, that would be ASA? Wait no, ASA is angle - side - angle (the side is included between the two angles). Wait, in \( \triangle AEC \) and \( \triangle BED \): \( \angle C=\angle B \), \( EC = EB \), \( \angle AEC=\angle BED \). So the side \( EC \) is between \( \angle C \) and \( \angle AEC \), and \( EB \) is between \( \angle B \) and \( \angle BED \). Wait, no, that's ASA? But the option is AAS or SAA. Wait, maybe the other pair. Wait, maybe the triangles are \( \triangle ACE \) and \( \triangle BDE \). Let's think again. The vertical angles are equal (\( \angle AEC=\angle BED \)). We have a marked angle at \( C \) and \( B \) (so \( \angle C=\angle B \)), and a marked side ( \( EC = EB \)). Wait, no, AAS: two angles and a side not between them. Wait, if we have \( \angle C=\angle B \), \( \angle A=\angle D \) (since the sum of angles in a triangle is \( 180^\circ \), if two angles are equal, the third is equal), and \( EC = EB \) (or another side). Wait, maybe the correct congruence is AAS (Angle - Angle - Side). Let's eliminate the other options: AAA only shows similarity, not congruence. ASS/SSA is not a valid congruence criterion. HL is for right triangles. SAS is side - angle - side (included angle). ASA is angle - side - angle (included side). So the correct one is AAS or SAA.

Answer:

AAS or SAA