Answer:
2. No, the triangles can't be proven congruent
3. yes, SAS; ΔSTV ≅ ΔSUV
4. yes, SSS; ΔNMQ ≅ ΔNPQ
5. No, the triangles can't be proven congruent
6. yes, SAS; ΔXWZ ≅ ΔXYZ
7. | Reasons |
1. | given (note this is a side) |
2. | given (note this is a side) |
3. | given |
4. | definition of a midpoint (a midpoint bisects the line it is one because it is equidistant from the two endpoints; basically, the two pieces of a line bisected by a midpoint will always be equal) |
5. | SSS Theorem (the two givens beside the midpoint were two sets of equal corresponding sides; since we have three sets of corresponding sides equal, the theorem used here is the SSS Theorem) |
Step-by-step explanation:
Here's a quick review of the two theorems mentioned in this worksheet:
- Side-Side-Side Theorem: in reference to congruency, this theorem states that if the three sides of one triangle are equal to the respective sides of another triangle, then the two triangles are congruent.
- What about SAS? The letters are ordered in that way for a reason: the Side-Angle-Side Theorem tells us that if we have two triangles, and a set of two corresponding sides and their included angle are equal, then the triangles are congruent.
- By included angle, we mean the angle between two sides.
I know, jaelee04, I'm sorry, this explanation is a bit short, but email me and I'll send you my full answer. The warning is that it's really long!
