A conjecture and the paragraph proof used to prove the conjecture are shown.
2 answers:
Answer with explanation:
Given: E is the mid point of DF.
Prove: 2 DE=D F
Proof with explanation:
It is given that is mid point of
.
1.→
So,
-------------------------By Definition of mid point
2.→ DE=E F----------------Segment Congruence Postulate
3.→DE+E F=D F ----------------Segment Addition Postulate
4.→DE+DE=D F-------------By Substitution
5.→Simplifying gives
2 DE=D F
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For this case we have the following relationship between the volumes:
Where,
V2: Volume of the triangular prism after applying the scale factor on each side
V1: Original volume of the triangular prism
k: scale factor
Substituting values we have:
Rewriting:
Answer:
the volume of the prism if each side is dilated by a factor of 1/3 will be
V = 1 cubic unit
Where,
V2: Volume of the triangular prism after applying the scale factor on each side
V1: Original volume of the triangular prism
k: scale factor
Substituting values we have:
Rewriting:
Answer:
the volume of the prism if each side is dilated by a factor of 1/3 will be
V = 1 cubic unit