SOLUTION: Given: ABCDEF is a regular hexagon Prove that adcf is a rectangle in a paragraph proof note that the diagram is a hexagon with labels ABCDEF and starting from the top right corne

Question 1143287: Given: ABCDEF is a regular hexagon
Prove that adcf is a rectangle in a paragraph proof
note that the diagram is a hexagon with labels ABCDEF and starting from the top right corner is A and it continues in alphabetical order. there are two segments FD and AC. please hurry, it’s a timed test!
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

ABCDEF is a regular hexagon, so all the side lengths are the same.

The interior angles of a regular hexagon are each 120 degrees.

Triangles ABC and DEF are isosceles, because all the side lengths of the hexagon are congruent.

Angles B and E are each 120 degrees; that makes angles BAC, BCA, EDF, and EFD each 30 degrees.

And that makes angles ACD, CDF, DFA, and FAC all right angles.

And that makes ACDF a rectangle.

Note your statement of the problem says to show that ADCF is a rectangle; it is not....
RELATED QUESTIONS
Given that polygon ABCDEF is a regular hexagon, prove that AC is congruent to... (answered by ikleyn)

GIVEN: ABCDEF is a regular hexagon PROVE: triangle ABC congruent to triangle... (answered by Mathtut)

If ABCDEF is a regular hexagon, how to calculate... (answered by CharlesG2)

What is the difference between a regular hexagon, equiangular hexagon and equilateral... (answered by solver91311)

ABCDEF is a regular hexagon, and PQR is an equilateral triangle. What is the ratio of the (answered by MathLover1,greenestamps)

ABCDEF is a regular hexagon. ABXY isa a square inside the hexagon. Find a. ∠XBC b.... (answered by solver91311)

Using a geometric proof, show that, in a regular polygon ABCDEF, (answered by Edwin McCravy)
Using a geometric proof, show that in a regular polygon ABCDEF , (answered by Edwin McCravy)
Find the length AC in regular hexagon ABCDEF if the perimeter of the hexagon is... (answered by CubeyThePenguin)