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Nezavi [6.7K]
3 years ago
12

Diagonals AC and BD form right angles at point M in parallelogram ABCD. Prove ABCD is a rhombus.

Mathematics
2 answers:
Tanya [424]3 years ago
5 0
1. Consider the parallelogram ABCD drawn in the 1. figure attached.

2. The diagonals of a parallelogram bisect each other, so AM=MC and BM=MD


3. In triangle ABC, BM is an altitude (BM perpendicular to AC), but also a median (AM=MC). An altitude is also a median only when the triangle is isosceles, so AB=BC 

similarly, in triangle BCD, CM is both an altitude and a median.Thus, BCD is an isosceles triangle so BC=CD.

4. AB= DC (opposite sides of a parallelogram are equal), similarly BC=DA

5. So ABCD is a quadrilateral, with all 4 sides equal in length. Thus ABCD is a rhombus. 

BabaBlast [244]3 years ago
5 0

The correct answer is:

B. △AMB ≅ △CMB ≅ △CMD ≅ △AMD

|Huntrw6|

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How can i solve 8(3a+6)=9(2a-4)
jeka57 [31]

Answer:

-14

Step-by-step explanation:

1.  Carry out the indicated multiplication, obtaining 24a + 48 = 18a - 36.

2.  Combine like terms:  6a = -84.

3.  Divide both sides by 6 to isolate a:  a = -84/6 = -14


8 0
3 years ago
A bicyclist travels at a constant speed of 18 miles per hour for a total of 27minutes. Choose the function, the domain and the r
snow_lady [41]

Answer:

domain is (xo ≤ x ≤ 0.45 )

range is  (xo ≤ y ≤ 8.1 )

Step-by-step explanation:

given data

constant speed = 18 miles per hour

total time = 27 minutes = 0.45 hour

solution

we consider here  Domain number of hours   = x and Range distance traveled  = y

we apply here distanace formula that is

Distance = speed × time    .........................1

put here value

Distance = 18 × 0.45 = 8.1 miles

and no of hours x = 0 to 0.45 hours

so here

So domain is (xo ≤ x ≤ 0.45 )

and

Distance is 0 to 8.1 miles

So range is  (xo ≤ y ≤ 8.1 )

4 0
3 years ago
A random number from 1 to 5 is selected
shutvik [7]

Answer:

Relative frequency of selecting a 2 = 8/50 = 0.16

Relative frequency of selecting a 3 = 14/50 = 0.28

Step-by-step explanation:

When we have a given experiment with given outcomes (such that each time that we perform the experiment, one outcome happens) the relative frequency of a given outcome is the quotient between the number of times that that outcome happened, and the total number of times that the experiment was performed.

Here the experiment is selecting a random number between 1 and 5, and it is performed 50 times.

Out of these 50 times, the outcome "2" appears 8 times.

Then the relative frequency of selecting the number 2 is:

f(2) = 8/50 = 0.16

And of these 50 experiments, the outcome "3" appears 14 times.

Then the relative frequency of selecting the number 3 is:

f(3) = 14/50  = 0.28

7 0
3 years ago
What is the modulus of |9+40i|?
Talja [164]

Answer:

41

Step-by-step explanation:

We know that complex numbers are a combination of real and imaginary numbers

Real part is x and imaginary part y is multiplied by i, square root of -1

Modulus of x+iy = \sqrt{x^2+y^2}

Here instead of x and y are given 9 and 40

i.e. 9+40i

Hence to find modulus we square the coefficients add them and then find square root

|9+49i| =\sqrt{9^2+40^2} =\sqrt{1681}

By long division method we find that

|9+40i| =41


6 0
3 years ago
Read 2 more answers
Will give brainliest!!! pls help with all questions
Mila [183]
It would be a lot better if you zoomed in for these since it’s nearly impossible to read.
4 0
2 years ago
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