how do we indicate the congruence at two triangles with two sides and the contained angle of the one equal two corresponding sides and the corresponding contained angle of the other ?
To indicate congruence between two triangles based on the given criteria, you can use the ASA (angle-side-angle) congruence criterion. Here's how you can apply it:
1. Start by identifying the two triangles that you want to prove congruent. Let's call them triangle ABC and triangle DEF.
2. Check if the given side and angle measurements satisfy the conditions for ASA congruence. In this case, it means that for triangle ABC and triangle DEF to be congruent, you need to have the following conditions:
a. Side-Side-Side (SSS): Two corresponding sides of triangle ABC should be equal in length to two corresponding sides of triangle DEF.
b. Angle-Side-Angle (ASA): The angle between the two equal sides of triangle ABC should be equal to the corresponding angle between the two equal sides of triangle DEF.
3. Verify that the two given sides in triangle ABC are congruent to the corresponding sides in triangle DEF. If they are not equal, the triangles are not congruent using the ASA criterion, and you will need to consider a different method.
4. Next, verify that the angle between the congruent sides in triangle ABC is equal to the corresponding angle between the congruent sides in triangle DEF. If these angles are congruent, then you can conclude that the two triangles are congruent by ASA criterion.
Remember, it is crucial to verify both the side lengths and angle measurements to determine congruence using the ASA criterion. If either the side lengths or angle measurements do not match, the triangles cannot be proven congruent using this method.