Which shows two triangles that are congruent by asa

The four options are attached below


Second attachment is the correct choice

Explanation:
ASA (angle-side-angle) means that two angles and the included side between them in the first triangle are congruent to the corresponding two angles and the included side between them in the second triangle

Now, let's check the choices:
First attachment:
It shows that two sides and the included angle between them in the first triangle is congruent to the corresponding two sides and the included angle between them in the second one. This is congruency by SAS. Therefore, this option is incorrect

Second attachment:
It shows that two angles and the included side  between them in the first triangle is congruent to the corresponding two sides and the included angle between them in the second triangle. This is congruency by ASA. Therefore, this option is correct

Third attachment:
It shows that the three angles in the first triangle are congruent to the corresponding three angles in the second one. This is not enough to prove congruency. Therefore, this option is incorrect

Fourth attachment:
It shows that the three sides in the first triangle are congruent to the corresponding three sides in the second one. This is congruency by SSS. Therefore, this option is incorrect.

Based on the above, the second attachment is the only correct one

Hope this helps :)

The second one, as shown in the attached picture.

Further explanationThe ASA (Angle-Side-Angle) postulate for the congruent triangles: two angles and the included side of one triangle are congruent to two angles and the included side of another triangle; the included side properly represents the side between the vertices of the two angles. The SAS (Side-Angle-Side) postulate for the congruent triangles: two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle; the included angle properly represents the angle formed by two sides.The SSS (Side-Side-Side) postulate for the congruent triangles: all three sides in one triangle are congruent to the corresponding sides within the other.The AAS (Angle-Angle-Side) postulate for the congruent triangles: two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.

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Notes

The angle-side-side postulate for the congruent triangles doesn't exist because an angle and two sides don't guarantee that two triangles are congruent. If two triangles have two congruent sides and a congruent non-included angle, then triangles don't seem to be necessarily congruent. This can be why there's no side-side-angle (SSA) and there's no angle-side- side postulate.The AAA (angle-angle-angle) postulate for congruent triangles does not work because having three corresponding angles of equal size is not enough to prove congruence. This principle is usually used for the similarity of two triangles.Learn moreAbout the lengths of the legs of the triangle About vertical and supplementary angles    Calculate the measures of the two angles in a right triangle