What else must you know to prove the triangles congruent by ASA? By SAS?
To prove triangles congruent by ASA (Angle-Side-Angle) and SAS (Side-Angle-Side), you must know the following:
1. ASA Congruence: To prove two triangles congruent using the ASA criterion, you need to have the information about the following:
a. Two pairs of corresponding angles are congruent.
b. The included side (the side between the corresponding angles) is congruent in both triangles.
2. SAS Congruence: To prove two triangles congruent using the SAS criterion, you need to have the information about the following:
a. Two pairs of corresponding sides are congruent.
b. The included angle (the angle between the corresponding sides) is congruent in both triangles.
In both cases, it is crucial to match corresponding parts of the triangles explicitly and mention why they are congruent.
To prove triangles congruent by ASA (Angle-Side-Angle), you must know the following:
1. The measure of two angles in one triangle that are equal to the corresponding two angles in the other triangle.
2. The length of the side between these two angles in one triangle is equal to the length of the corresponding side in the other triangle.
To prove triangles congruent by SAS (Side-Angle-Side), you must know the following:
1. The length of two sides of one triangle that are equal to the corresponding two sides of the other triangle.
2. The measure of the angle included between these two sides in one triangle is equal to the measure of the corresponding angle in the other triangle.
Both of these methods rely on comparing corresponding angles and sides in two triangles. If the given information matches the criteria mentioned above, you can conclude that the triangles are congruent.