Point d is in the interior of △abc. line cd intersects ab at point m. prove that, if aadc=abdc, then cm is the median of △abc.

Proved

Step-by-step explanation:

Given that in a triangle ABC, a line Starting from vertex C through an interior point M meets the opposite side AB at the point D.

Also given that areas of ADC and BDC are equal.

We find that ADC and BDC are triangles with bases as the same line.  Hence altitude dropped from C would have the same height for both triangles

In other words, heights are equal.

ARea of triangle ADC = Area of triangle BDC

It follows D is the mid point of AB.

Or CM is the median of ABC

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

a

step-by-step explanation: