beginning at sea level a scuba diver dove 1 2/3 feet into the water , and then dove an additional 3 2/5 feet at what elevation i
1 answer:
The given details are illustrations of addition and subtractions of fractions. The scuba driver is at an elevation of ft below the sea level.
Given that:
--- the first dive
---- the additional dive
From the question, we understand that the diver starts at the sea level.
This is represented with 0ft.
So, the diver's elevation (d) is calculated as follows:
--- we use subtraction because the diver is below the sea level
So, we have:
Convert fractions
Take LCM
Reduce fraction
The above value means that the diver's elevation is at ft below the sea level.
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Answers:
- Similar = Yes, they are similar
- How: AA similarity
- Similarity statement: triangle HGF ~ triangle HMN
The ~ mark means "similar"
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The red angle markings tell us which angles are congruent to one another. We have these two pairs of congruent angles
- angle H = angle H (both triangles unfortunately reuse H) by the single arc marking
- angle G = angle M, by the double arc markings
Because we have two pairs of congruent angles, we use the AA similarity theorem. AA stands for angle angle. We could use three pairs, but two pairs is the minimum needed for similarity statements.
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To figure out what goes in the third answer box, note how the order HGF is given to us. The order is important.
We have H first, G second, F third.
H being first, and it having a single arc, means that whatever has a single arc on the other triangle must be first. That would be H. Unfortunately they reuse angle H which makes things confusing a bit.
G is second in HGF, and G has the double arc marking. Note how M also has this double arc marking. Therefore we have M second in the answer. So far we have HM as part of the third answer.
The only thing left is N. Therefore, we have triangle HMN as the answer for the third box.
Put another way, we have these pairings:
- H (single arc mark) = H (single arc mark)
- G (double arc mark) = M (double arc mark)
- F (no marking) = N (no marking)
This is why the order is important. So we can see how the angles pair up in the order that they do.
This is why triangle HGF is similar to triangle HMN.
We can write that as triangle HGF ~ triangle HMN
The ~ mark means "similar"
We don't have enough information to prove that the triangles are congruent or not. So we cannot say . Your teacher made a typo when using the congruence symbol
Instead, it should be