All categories

2 years ago

Prove that the diagonals of a parallelogram bisect each other. The midpoints are the same point, so the diagonals _____

Mathematics

1 answer:

Molodets [167]2 years ago

8 0

Answer:

Below

Step-by-step explanation:

To prove that the diagonals bisect each other we should prove that they have a common point.

From the graph we notice that this point is E.

ABCD is a paralellogram, so E is the midpoint of both diagonals.

●●●●●●●●●●●●●●●●●●●●●●●●

Let's start with AC.

● A(0,0)

● C(2a+2b,2c)

● E( (2a+2b+0)/2 , (2c+0)/2)

● E ( a+b, c)

●●●●●●●●●●●●●●●●●●●●●●●●

BD:

● B(2b,2c)

● D(2a,0)

● E ( (2a+2b)/2 , 2c/2)

● E ( a+b ,c)

●●●●●●●●●●●●●●●●●●●●●●●●●

So we conclude that the diagonals bisect each others in E.

You might be interested in

In triangle ABC, sin A = 24 25 . Which other expression has a value of 24 25 ? A) sin B B) cos A C) cos B D) tan A

Svetradugi [14.3K]

I think it's B hope I helped

8 0

2 years ago

Read 2 more answers

Given regular pentagon ABCDE, what are the coordinates of vertex C?

nata0808 [166]

Answer: a

Step-by-step explanation: C is in quadrant 1 and quadrant 1 is (+,+)

6 0

2 years ago

Water is poured into a conical paper cup at the rate of 3/2 in3/sec (similar to Example 4 in Section 3.7). If the cup is 6 inche

aliya0001 [1]

Answer:

The water level rising when the water is 4 inches deep is $\frac{3}{8\times \pi} inch/s$ .

Step-by-step explanation:

Rate of water pouring out in the cone = R= $\frac{3}{2} inch^3/s$

Height of the cup = h = 6 inches

Radius of the cup = r = 3 inches

$\frac{r}{h}=\frac{3 inch}{6 inch}=\frac{1}{2}$

r = h/2

Volume of the cone = $V=\frac{1}{3}\pi r^2h$

$V=\frac{1}{3}\pi r^2h$

$\frac{dV}{dt}=\frac{d(\frac{1}{3}\pi r^2h)}{dt}$

$\frac{dV}{dt}=\frac{d(\frac{1}{3}\pi (\frac{h}{2})^2h)}{dt}$

$\frac{dV}{dt}=\frac{1}{3\times 4}\pi \times \frac{d(h^3)}{dt}$

$\frac{dV}{dt}=\frac{1\pi }{12}\times 3h^2\times \frac{dh}{dt}$

$\frac{3}{2} inch^3/s=\frac{1\pi }{12}\times 3h^2\times \frac{dh}{dt}$

h = 4 inches

$\frac{3}{2} inch^3/s=\frac{1\pi }{12}\times 3\times (4inches )^2\times \frac{dh}{dt}$

$\frac{3}{2} inch^3/s=\pi\times 4\times \frac{dh}{dt} inches^2$

$\frac{dh}{dt}=\frac{3}{8\times \pi} inch/s$

The water level rising when the water is 4 inches deep is $\frac{3}{8\times \pi} inch/s$ .

6 0

2 years ago

Shelly bought a house five years ago for $150,000 and obtained an 80% loan. Now the home is worth $140,000 and her loan balance

LiRa [457]

Answer:

The current equity is $32,000

Step-by-step explanation:

Here, we are to calculate the current equity of the House

Value of house initially is $150,000

loan borrowed is 80% of this

= 80/100 * 150,000 = $120,000

Now the house value is 140,000 and the loan amount is reduced to 12,000

The outstanding loan amount to pay would be 120,000-12,000 = 108,000

The current equity is thus = Assets - liability = 140,000-108,000 = $32,000

5 0

2 years ago

Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select t

tankabanditka [31]

Help me I’m on the test review and I don’t get it someone help stupid edgenuity teachers are too lazy to teach us themselves

4 0

2 years ago

Read 2 more answers