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VladimirAG [237]
4 years ago
14

Prove that a parallelogram is a square iff its diagonals are both congruent and perpendicular

Mathematics
1 answer:
Juliette [100K]4 years ago
6 0
Consider the parallelogram shown below.
The lengths of the sides are a and b.
The lengths of the diagonals are 2x and 2y.

Because the diagonals are both congruent and perpendicular, therefore there are two right triangles as shown.
Note that x = y.
Because x = y, each right triangle is isosceles and has the angles 90°, 45° and 45°.

From the Pythagorean theorem,
For one right triangle,
a² = x² + y² = x² + x² = 2x².
For the other right triangle,
b² = y² + x² = x² + x² = 2x²

Therefore
a² = b²
a = b

It follows that all sides of the parallelogram are equal and each angle is
45+45 = 90°

Therefore the parallelogram is a square.

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A necklace regularly sells for $18.00. the store advertises a 15% discount. what is the sale price of the necklace in dollars
SSSSS [86.1K]
I can solve with 2 methods:

I. Because the discount is 15 % of 18 $ , the price will be (100-15=85) 85 % of 18 $
18*85/100= 15,3 $ ( the sale price)

II. The discount is 15 % of 18$
15*18/100= 2,7$  ( the discount)
then I decrease it from the regularly price
18$-2,7$=15,3 $ (the sale price)

Personally I believe the first is an easier method.
I hope you understand and you can apply this in every similary problem.



6 0
3 years ago
Help please! (no one was answering it in physics and i really need help)
aivan3 [116]

Let v_0 be the cat's speed just as it leaves the edge of the table. Then taking the point 1.3 m below the edge of the table to be the origin, the cat's horizontal position at time t is given by

x(t)=v_0t

and its height is

y(t)=1.3\,\mathrm m-gt^2

where g is 9.8 m/s^2, the magnitude of the acceleration due to gravity.

The time it takes for the cat to hit the ground is t with

0=1.3\,\mathrm m-gt^2\implies t=\sqrt{\dfrac{1.3\,\rm m}g}\approx0.36\,\mathrm s

(Unfortunately, this doesn't match any of the given options...)

The cat lands 0.75 m away (horizontally) from the edge of the table, so that its speed v_0 was

0.75\,\mathrm m=v_0(0.36\,\mathrm s)\implies v_0\approx2.08\dfrac{\rm m}{\rm s}

(Again, not one of the answer choices...)

I'm guessing there's either a typo in the question or answers.

6 0
3 years ago
What are the solutions to the system of equations graphed below? Select all<br> that apply.
postnew [5]
Answer is A and B. Solutions are where the two graphs cross, so you just need to find those coordinates, which are (-5,-13) and (2,-6).
7 0
3 years ago
Read 2 more answers
The perimeter of a rectangle is 50 inches. The length of the rectangle is 10 inches. Which
VMariaS [17]

Answer:15

Step-by-step explanation:

Solve for w in the equation 2w + 10 =50.

8 0
3 years ago
ANSWER FOR BRAINLIEST AND 72 POINTS
kumpel [21]

Answer:

A

Step-by-step explanation:

the probability should always be the same unless the event is different.

6 0
3 years ago
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