Geometry Problem....?

Question

If a polygon has equal sides, it also has equal angles. Is this true?
If a polygon has equal angles, it also has equal sides? Is this true.

Can someone explain this to me?

Answer 1

Neither statement must be true. A rhombus is an example that contradicts the first statement, and a rectangle contradicts the second statement.

Answer 2

For a triangle this is true, but any other size polygon this is not true. Just take an equilateral triangle and try to change the angles from being equal without changing the sides from being equal. You will find this impossible. Now do this to a square which has equal sides and equal angles. you will find this much easier as you will get many different rhombuses.

Answer 3

I think the easiest way to think about this is that all polygons with equal sides can be broken down into a series of triangles with the sides going from a corner to the center. These triangles are identical so the two angles of the adjacent triangles that sum to make a corner will also be the same. Therefor all the angles will be the same.

When you try to parse some of the geometry problems like this try breaking the space down into pieces you can understand and see where you have relationships you can use. Most of the time that approach will work.

Answer 4

Both statements are false.

Counter example for 2nd statement:
Draw a rectangle with width 1 and length 2. Note all the angles are 90 degrees.

Counter example for 1st statement:
Draw a diamond with all the sides equal. The opposite angles will be equal, but the adjacent angles won't be.

Additional note: If you replace the word polygon with triangle in the statements, both will be true.

Answer 5

Question 1 - False. Take ten toothpicks. They have equal sides but you can push them together into a polygon of almost any shape so the angles are not necessarily equal.

Question 2. False. Take 6 toothpicks and make a regular hexagon. Now, take one half of it (having 3 toothpicks) and sort of move it into the other half so that you don't change any angles but the tooth picks overlap where they're meeting. They place where the 2 halves meet have overlapping toothpicks, the the sides are not equal but the angles are.This is hard to explain without pictures, but take the toothpicks & try to do what I'm saying.

Answer 6

Yes, both of those questions are true.

Try thinking about it this way:

Say your polygon is a triangle. As the sides grow in length, the angles expand in size of degrees. If all of the sides are the same length, then all of the angles must be the same number of degrees, because they "expanded" the same amount.

An example of such a triangle would be one that has all 3 angles at 60 degrees. All of the sides must be the same as well. Whereas, you can prove the opposite by using a triangle that you know doesn't have the same angle sizes.
For example: A right triangle that has angles 90 degrees, 60 degrees and 30 degrees.
One example of this type of triangle would have sides of length 3, 4 and 5. You can prove this by using the pythagorean theorem, or sin, cos, and tan.

Other types of polygons can be proven in similar ways. Any polygon that has all sides of the same length is considered to be "regular" and any "regular" polygon will have all of the same angles inside.

Answer 7

this is definitely true for example on a triangle.Let x= measure of side.
so it will be 3x=180 because the angle in a triangle should equal 180
divide both sides by three then you will have
x=60
therefore the measure of each sides is equal throughout.

Answer 8

No
Pretend the polygon you have in mind is made out of stiff equal segments connected by flexible hinges. Could you squash it or otherwise bend it out of shape? You could for example deform a square and turn it into a rhombus.

Answer 9

the truth is that for both questions it depends. So those two statements are NOT always true. it also depends if the polygon is regular or irregular.

Good Luck, though
Q-T pie

Answer 10

Yes, this is always true because between any two adjacent sides, you have one angle, and between any two adjacent angles, you have one side.