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3 years ago

To be considered similar, two polygons must have corresponding sides that are ______.

Mathematics

2 answers:

Bond [772]3 years ago

7 0

Corresponding sides must be proportional and corresponding angles are congruent.
LetterA

kifflom [539]3 years ago

6 0

Answer:

Option A). In proportion

Step-by-step explanation:

A).For two polygons which are similar they must have the corresponding sides in the same proportion and the angles will be congruent. So option A is correct.

B). Corresponding sides will not be congruent in similar polygons.

C). Corresponding sides will not be similar or same in size.

D). Sides will not be necessarily parallel in two similar polygons.

therefore Option A is the answer.

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3 years ago

determine whether the infinite geometric series converges or diverges. if it converges find its sum. 3-3/4+3/16-3/64+...

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3 years ago

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3 years ago

A rectangular lamina of uniform density is situated with opposite corners at (0,0) and (15,4). calculate its radii of gyration a

Sphinxa [80]

First, you have to find the moment of inertia along the x and y axes. Constant density is denoted as k.

$I_{x}= \int\limits^15_0\int\limits^4_0 {k y^{2} } \, dx dy= \frac{1}{3}k (15-4)^4=4880.33k$

$I_{y}= \int\limits^15_0\int\limits^4_0 {k x^{2} } \, dx dy= \frac{1}{3}k (15-4)^4=4880.33k$

Then, the radii of gyration for

x = √[I_x/m]
y = [I_y/m]

where m = k(15-4)² = 121k. Then,

x = y = [4880.33k/121k] = 40.33

I hope I was able to help you. Have a good day.

7 0

3 years ago

In order for a 25-gon to be regular

Elan Coil [88]

Answer:

d. All interior angles and all sides are parallel.

Explanation:

The question is incomplete.

The complete question is:

In order for a 25-gon to be regular, which of the following statements must be true?

a. The interior angles are congruent to their exterior angles.

b.All the diagonals are congruent.

c.Opposite pairs of sides are parallel.

d. All interior angles and all sides are congruent

<h2>Solution to the problem</h2>

A 25-gon is a polygon with 25 sides.

By definiton all sides and all angles of a regular polygon are equal. Hence, you can assert promptly that the correct anwer is the last choice: d. All interior angles and all sides are congruent.

As for the other choices you can analyze each one in this way.

a. The interior angles are congruent to their exterior angles.

The exterior angles are the angles formed by the extension of a side and the next side.

The exterior angles of a polygon sum 360°, then if the polygon is regular the measure of each exterior angle 360° divided by the number of sides.

For the regular 25-gon, that is: 360º/25 = 14.4º.

On the other hand, an exterior angle and the interior angle next to are supplementary. Thus, the measure of the interior angle will be 180º - 14.4º = 165.6º. Clearly, they are not congruent.

b. All the diagonals are congruent.

The diagonals are the sements that joint two non-consectuive sides. There are many differnt diagonals, and most of them have different lengths. Hence, this is false.

c.Opposite pairs of sides are parallel

Only poygons with an even number of sides have opposite side paralles. For instance, square and hexagon. Imagin a triangle or a pentagon: they cannot have parallel opposite sides.

Hence, this is false too.

The only true stament is the last one, as stated and explained above.

5 0

4 years ago