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kiruha [24]
3 years ago
7

Parallelogram ABCD is given. Draw line EF so that it goes through the vertex A. Point E lies on the side BC and point F lies on

the extension of DC. Prove that ABE is similar FCE

Mathematics
1 answer:
tresset_1 [31]3 years ago
7 0

Answer:

The proof is explained step-wise below :

Step-by-step explanation :

For better understanding of the solution see the attached figure :

Given : ABCD is a Parallelogram ⇒ AB ║ DC and AD ║ BC

Now, F lies on the extension of DC. So, AB ║ DF

To Prove : ΔABE is similar to ΔFCE

Proof :

Now, in ΔABE and ΔFCE

∠ABE = ∠FCE ( alternate angles are equal )

∠AEB = ∠FEC ( Vertically opposite angles )

So, by using AA postulate of similarity of triangles

ΔABE is similar to ΔFCE

Hence Proved.

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standard automobile license plates in a country display 3 numbers, followed by 2 letters, followed by 2 numbers. how many differ
RoseWind [281]

The system of standard automotive license plates allows for a variety of standard plates is 39917124 ways.

<h3>Define the term permutation?</h3>
  • The number of potential arrangements for a given set is assessed mathematical terms, but this procedure is referred to as permutation.
  • The arrangement's order is essential when using permutations.

For the stated data;

Standard car license plates in a nation typically have 3 digits, 2 letters, and 2 numbers.

There are total 9 digits (0 - 9).

There are total 26 letter (A - Z)

Repetitions of letters and numbers given allowed.

Thus, numbers and the letters ca be arranged as;

1st place = 9 ways.

2nd place = 9 ways.

3nd place = 9 ways.

4th place = 26 ways.

6th place = 26 ways.

7th place = 9 ways.

8th place = 9 ways.

Total ways = 9×9×9×26×26×9×9

Total ways = 39917124

Thus, the system of standard automotive license plates allows for a variety of standard plates is 39917124 ways.

To know more about the permutation, here

brainly.com/question/1216161

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5 0
1 year ago
I need help please it’s due tomorrow.......
Sholpan [36]
Let
x-------> the width of the rectangular area
y------> the length of the rectangular area

we know that
y=x+15------> equation 1
perimeter of a rectangle=2*[x+y]
2x+2y <= 150-------> equation 2

substitute 1 in 2
2x+2*[x+15] <=150--------> 2x+2x+30 <=150----> 4x <=150-30
4x <= 120---------> x <= 30
the width of the rectangular area is at most 30 ft
y=x+15
for x=30
y=30+15------> y=45
 the length of the rectangular area is at most 45 ft

see the attached figure
the solution is<span> the shaded area</span>

4 0
3 years ago
Solve the inequality 12x &lt; 22 + x.
earnstyle [38]

Answer:

12x<22+x

11x<22

x<2

8 0
3 years ago
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An orange has about 1/4 cups of juice.Hiw many Oranges are needed to make 2 1/2 cups of juice?
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Answer:

10/4 cups of juice

Step-by-step explanation:

4/4 = 1

so 4/4 + 4/4 = 2

and 1/2 = 2/4

then add

4/4 + 4/4 + 2/4 = 10/4

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When ABC was dialed by a scale factor of 2, centered at the origin, the result was its image A'B'C' shown on the coordinates pla
sweet-ann [11.9K]

Answer:

Step-by-step explanation:

In dilation, the image and the original are similar, in that they are the same shape but not necessarily the same size. They are not congruent because that requires them to be the same shape and the same size, which they are not (scale factor is 2)

vertices of ABC are A(-2,2), B(-2,3), and C(1,2)

If we multiply by 2 from original to image,

then from image to original we divide by 2

4 0
3 years ago
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