For any line, if you draw two right triangles using the line as the hypotenuse, can the triangles be congruent? Why or why not?
Do they have to be congruent? Why or why not?
ANSWER ALL OF THE QUESTIONS OR DONT ANSWER AT ALL THANK YOU.
ANSWER ALL OF THE QUESTIONS OR DONT ANSWER AT ALL THANK YOU.
1 answer:
Answer:
The triangles can be congruent but not always.
The triangles do not have to be congruent, but they have to be similar.
Step-by-step explanation:
See the attached diagram with this answer.
For any line (say OP), if you draw two right triangles ( Δ ABC and Δ A'B'C') using the line, OP as the hypotenuse, then the triangles can be congruent. This will be only when AC = A'C'.
That means if we draw two right triangles using the same length of a straight line as hypotenuse, then only the two right triangles will be congruent.
Now, If AC = A'C' then automatically, it becomes AB = A'B' and BC = B'C' and then by SSS criteria, the triangles Δ ABC and Δ A'B'C' will be congruent i.e. Δ ABC ≅ Δ A'B'C'.
But the triangles Δ ABC and Δ A'B'C' do not have to be congruent but they have to be similar.
Because,
If this ratio becomes 1 : 1 then only those triangle will be congruent otherwise they will be similar only. (Answer)
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Answer:
(a) The standard deviation of the amount spent is $3229.18.
(b) The probability that a household spends between $4000 and $6000 is 0.2283.
(c) The range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.
Step-by-step explanation:
We are given that the average annual amount American households spend on daily transportation is $6312 (Money, August 2001). Assume that the amount spent is normally distributed.
(a) It is stated that 5% of American households spend less than $1000 for daily transportation.
Let X = <u><em>the amount spent on daily transportation</em></u>
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = average annual amount American households spend on daily transportation = $6,312
= standard deviation
Now, 5% of American households spend less than $1000 on daily transportation means that;
P(X < $1,000) = 0.05
P( <
) = 0.05
P(Z < ) = 0.05
In the z-table, the critical value of z which represents the area of below 5% is given as -1.645, this means;
= 3229.18
So, the standard deviation of the amount spent is $3229.18.
(b) The probability that a household spends between $4000 and $6000 is given by = P($4000 < X < $6000)
P($4000 < X < $6000) = P(X < $6000) - P(X $4000)
P(X < $6000) = P( <
) = P(Z < -0.09) = 1 - P(Z
0.09)
= 1 - 0.5359 = 0.4641
P(X $4000) = P(
) = P(Z
-0.72) = 1 - P(Z < 0.72)
= 1 - 0.7642 = 0.2358
Therefore, P($4000 < X < $6000) = 0.4641 - 0.2358 = 0.2283.
(c) The range of spending for 3% of households with the highest daily transportation cost is given by;
P(X > x) = 0.03 {where x is the required range}
P( >
) = 0.03
P(Z > ) = 0.03
In the z-table, the critical value of z which represents the area of top 3% is given as 1.88, this means;
x = $6312 + 6070.86 = $12382.86
So, the range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.