Answer:
2. No, the triangles can't be proven congruent
3. yes, SAS; Δ<em>STV</em> ≅ Δ<em>SUV</em>
4. yes, SSS; Δ<em>NMQ</em> ≅ Δ<em>NPQ</em>
5. No, the triangles can't be proven congruent
6. yes, SAS; Δ<em>XWZ</em> ≅ Δ<em>XYZ</em>
7. | <em>Reasons</em> |
1. | <em>given</em> (note this is a <em>side</em>) |
2. | <em>given</em> (note this is a <em>side</em>) |
3. | <em>given</em> |
4. | <em>definition of a midpoint</em> (a midpoint <em>bisects</em> the line it is one because it is <em>equidistant</em> from the two endpoints; basically, the two pieces of a line bisected by a midpoint will <em>always</em> be equal) |
5. | <em>SSS Theorem</em> (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 <em>congruency</em>, 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 <em>Side-Angle-Side</em> 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 <em>included angle</em>, we mean the angle <u><em>between</em></u><em> two sides</em>.
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!
