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2 years ago

Why do vertices connected by a diagonal of a polygon have to be nonconsecutive?

Mathematics

2 answers:

Sever21 [200]2 years ago

8 0

Because consecutive vertices are already connected by the edges of the polygon.

oksian1 [2.3K]2 years ago

8 0

Answer:

Basically, a segment which connects two consecutive vertices is not a diagonal, it's actually a side of a polygon.

So, in order to get a diagonal, you need to unit two nonconsecutive vertices, that way you won't get a side but a diagonal.

Actually, a diagonal of a polygon is defined as a segment which connects two nonconsecutive vertices.

Therefore, by definition, a diagonal must connect two nonconsecutive vertices.

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Math work pls help :)

solong [7]

Answer:

the theorum used here is sas one

8 0

2 years ago

Find the length of a rectangle if its

Alina [70]

Answer: L = 29cm

Step-by-step explanation:

Let's go!!

To find any rectangle area, you have to apply this formula: A = L . w , where L is the length and w is the width.

So, we have w = L - 13 (the width is 13 less than the Length) and then, perimeter is 90 cm.

Well, I hope you remember that the perimeter of rectangle is 2L + 2W. In this case, 2L + 2w = 90

Then, you might to solve this system of equation:

2L + 2w = 90

w = L - 13

Simplifying the first equation, you'll have L + w = 45 (you can divide everything of 2).

Our new system:

L + w = 45

w = L - 13

Using the substituition method:

L + L - 13 = 45

2L = 58

L = 29 cm

the width is 29 - 13 = 16 cm

4 0

3 years ago

In the isosceles triangle, find a and b if you knew the perimeter was 20x+35

Zanzabum

Answer:

a=8

b=17

Step-by-step explanation:

Isoceles means we will have 2 congruent sides in this triangle.

So it appears we are to assume it is sitting on its base which means that other side has measurement ax+9 as well

So we have the sum of the 3 sides is the perimeter.

That means we have the equation:

(ax+9)+(ax+9)+(4x+b)=20x+35

Combine like terms:

(a+a+4)x+(9+9+b)=20x+35

(2a+4)x+(18+b)=20x+35

This implies 2a+4=20 and 18+b=35.

2a+4=20

Subtract 4 on both sides:

2a=16

Divide both sides by 2:

a=8

18+b=35

Subtract 18 on both sides:

b=17

So a=8 and b=17.

3 0

3 years ago

Can someone help me pls

atroni [7]

Answer:

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I wanna believe

Hit you with some truth

When we're together

I can't even lie

You and me got chemistry

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Feel it when you're close to me

And out of reach

And in between

We got la la la, lots of good vibrations

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And out of reach

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6 0

3 years ago

A statue is mounted on top of a 21 foot hill. From the base of the hill to where you are standing is 57feet and the statue subte

puteri [66]

Please find the attached diagram for a better understanding of the question.

As we can see from the diagram,

RQ = 21 feet = height of the hill

PQ = 57 feet = Distance between you and the base of the hill

SR= h=height of the statue

$\angle SPR=7.1^0$ =Angle subtended by the statue to where you are standing.

$\angle x$ = $\angleRPQ$ which is unknown.

Let us begin solving now. The first step is to find the angle $\angle x$ which can be found by using the following trigonometric ratio in $\Delta PQR$ :

$tan(x)=\frac{RQ}{PQ}=\frac{21}{57}$

Which gives x to be:

$x=tan^{-1} (\frac{21}{57})\approx 20.22^{0}$

Now, we know that $\angle x$ and $\angle SPR$ will get added to give us the complete angle $\angle SPQ$ in the right triangle $\Delta PQS$ .

We can again use the tan trigonometric ratio in $\Delta PQS$ to solve for the height of the statue, h.

This can be done as:

$tan(\angle SPQ)=\frac{SQ}{PQ}$

$tan(7.1^0+20.22^0)=\frac{SR+RQ}{PQ}$

$tan(27.32^0)=\frac{h+21}{57}$

$\therefore h+21=57\times tan(27.32^0)$

$h\approx8.45 feet$

Thus, the height of the statue is approximately, 8.45 feet.

5 0

2 years ago

Read 2 more answers