Triangle Congruence - Answers (two sides, one angle)
Question 1. Yes, you can construct two non-congruent triangles, see the picture. Invalid congruence condition: If two sides and one angle of one triangle are congruent to two sides and one angle of another triangle, these two triangles may NOT be congruent.
Question
2. No, you only can create triangles that are congruent. It is a
valid
congruence condition:
If two sides and included angle of one
triangle are congruent to two
sides and included angle of another triangle, then these two triangles
are congruent.
Question 3. Yes, you
can construct two non-congruent
triangles, even when corresponding objects are congruent, see the
picture. Invalid congruence condition: If two sides of one triangle are congruent
to two sides of another triangle and a pair of corresponding angles are
congruent, then the two triangles may NOT be congruent.
Question 4. No, you only can create triangles that are congruent. It is a valid congruence condition: If two sides of one triangle are congruent to two sides of another triangle, and a pair of angles opposite the longer side are congruent, then the two triangles are congruent.