The box plot compares Marta’s and Ani’s diving scores in the first several meets of the season. Based on the data in the box plo
2 answers:
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Answer:
Given: ∆ABC with the altitudes from vertex B and C intersect at point M, so that BM = CM.
To prove:∆ABC is isosceles
Proof:-Let the altitudes from vertex B intersects AB at D and from C intersects AC at E( with reference to the figure)
Consider ΔBMC where BM=MC
Then ∠CBM=∠MCB......(1)(Angles opposite to equal sides of a triangle are equal)
Now Consider ΔDMB and ΔCME
∠D=∠E.......(each 90°)
BM=MC...............(given)
∠CME=∠BMD........(vertically opposite angles)
So by ASA congruency criteria
ΔDMB ≅ ΔCME
∴∠DBM=∠MCE........(2)(corresponding parts of a congruent triangle are equal)
Adding (1) and (2),we get
∠DBM+∠CBM=∠MCB+∠MCE
⇒∠DBC=∠BCE
⇒∠B=∠C⇒AB=AC(sides opposite to equal angles of a triangle are equal)⇒∆ABC is an isosceles triangle .
Answer:
They need 130 yds to build up the fence.
Step-by-step explanation:
Attached you can find a picture that will guide the explanation. We will assume that each line is supposed to be a fence. We will assume also that the diagonals that cross any subfield that has the same vegetable is unnecessary. That is that the diagonal of the tomatoes and the watermelon are not going to be built.
Recall that the red peppers area is a right triangle. So, using pythagora's theorem, we have that
so
which gives us that b = 9.
On the same fashion, the diagonal of the spinach-celery sector is . Recall that the field is a rectangle, so the perimeter of the outter fence is 2*(12+6)+2*(8+9) = 70 yds. Then, the total perimeter is given by
outter fence (70)+
fence spinach-watermelon (8) +
fence red peppers-watermelon(12)+
fence red peppers-carrots (15)+
fence carrots-tomatoes (9)+
fence celery-tomatoes(6) +
fence spinach-celery(10)
= 130 yds
(if the diagonals of tomatoes and watermelon are added, the same procedure applies. watermelon diagonal is 14.42 yds and tomatoes diagonal is 10.81 yds)
