Question

2. You are given the picture of two triangles below. Are the two triangles congruent? Explain. If they are congruent, you must provide in your explanation the following:

•All parts that are congruent (with the correct congruency statement)
•An explanation of why those parts are congruent
•The theorem that determines the triangles are congruent based on the parts that are congruent If they are not congruent, you must provide in your explanation the following:
•All parts that are congruent (with the correct congruency statement) and the reason they are congruent
•Identify two parts that need to be congruent to make the triangles congruent
•The theorem that determines the triangles are congruent based on the parts that are congruent

HELP PLEASE DUE TONIGHT DONT JUST ANSWER FOR POINTS!!!!!!!​

Answer 1

Yes these triangles are congruent.

Explanation:

These triangles are congruent because the Angle Side Angle (ASA) states that triangles are congruent if their 2 corresponding angles and one included side are equal. Line A-E and line D-B show equal angles. The mark on the line A-E indicates that both of the sides are equal

Hopes this helps? I am not sure if I got everything.

Answer 2

analyze the congruency of the two triangles in the picture, presumably triangles ABC and DEC.

For triangles to be congruent, they must satisfy one of the congruency theorems: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), or HL (Hypotenuse-Leg for right triangles).

Here's what we know:

1. AC = EC: Given as congruent.

2. Angle A = Angle E: Given as congruent because AB is parallel to DE, which by alternate interior angles theorem means angle A and angle E are equal.

3. Angle C: It is shared by both triangles (triangle ABC and triangle DEC), so it's congruent by the reflexive property.

With these three pieces of congruent information, we can now say that the triangles are congruent by the ASA (Angle-Side-Angle) postulate. This postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

So, to put it formally:

- Triangle ABC is congruent to triangle DEC (ΔABC ≅ ΔDEC) by the ASA postulate because:

- AC = EC (Given)

- Angle A = Angle E (Alternate interior angles are equal since AB || DE)

- Angle C = Angle C (Shared angle, reflexive property of congruence)

Thus, the triangles are congruent based on the parts that are congruent, as explained above.