MATH SOLVE

4 months ago

Q:
# Which shows two triangles that are congruent by ASA? γ

Accepted Solution

A:

The four options are attached below

Answer:

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 sideΒ 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 :)

Answer:

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 sideΒ 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 :)