What if I showed angles DEB and EBC to be equall

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In summary, to prove that ABCDE is a trapezium, you need to show that lines EB and DC are parallel. This can be done by picking a point F to the left of D along line CD and proving that DEB = EDF. Another way is to draw diagonals through the trapezium and prove that the alternate angles are equal. However, it should be noted that a trapezium does not necessarily have to have two non-parallel sides, as it can also be a parallelogram.
  • #1
m00c0w
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http://img298.echo.cx/img298/2145/pentagon8zw.png ABCDE is a regular pentagon, in the previous question I worked out angle AEB to be 36°.. the next question has asked to prove that BCDE is a trapezium but I don't know how to. I figured it might be to do with showing that the sum of the angles in BCDE = 360° but that doesn't necessarily prove it is a trapezium. What if I showed angles DEB and EBC to be equal.. does that prove it?

Many thanks.
 
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  • #2
You want to show that lines EB and DC are parallel. One way: pick a point F to the left of D along line CD, and show DEB = EDF.
 
  • #3
hello there

a trapezium needs to have two sides parallel to each other and the other two sides unparallel to each other, if you want you could draw diagnals through the trapezium and prove that the alternate angles are equal that is prove that angle EBD= BDC
or anything similar to prove that it has two parallel sides

check out this simple link
http://www.icteachers.co.uk/children/sats/quadrilaterals.htm

Steven
 
  • #4
I have never heard that a trapezoid (trapezium) had to have the other two sides non-parallel. Mathworld and dictionary.com are ambiguous but wikipedia is clear that a trapezoid can also be a parallelogram.
http://en.wikipedia.org/wiki/Trapezoid
 
  • #5
BicycleTree said:
I have never heard that a trapezoid (trapezium) had to have the other two sides non-parallel. Mathworld and dictionary.com are ambiguous but wikipedia is clear that a trapezoid can also be a parallelogram.
http://en.wikipedia.org/wiki/Trapezoid


I knew i should have not erased what i originally wrote, well anyway i provided the link so that he doesn't get confused, well such a shape has a proper name a parallelogram which is a part of the family of quadrilaterals, and in this case all that is necessary is to prove that it has one pair of parallel sides to show that it is a trapezium
 

1. What does it mean to show angles DEB and EBC to be equal?

Showing angles DEB and EBC to be equal means that you have proven that the two angles have the same measure.

2. How can I show angles DEB and EBC to be equal?

There are several ways to show that angles DEB and EBC are equal. One method is to use the Angle-Angle-Side (AAS) postulate, where two angles and the included side of one triangle are congruent to two angles and the included side of another triangle. Another method is to use the Angle-Side-Angle (ASA) postulate, where two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.

3. Why is it important to show angles DEB and EBC to be equal?

Showing that angles DEB and EBC are equal is important because it helps to prove the congruence of two triangles. This can be useful in solving various mathematical problems and in constructing geometric figures.

4. What are some properties that can be used to show that angles DEB and EBC are equal?

Some properties that can be used to show that angles DEB and EBC are equal include the Vertical Angles Theorem, which states that vertical angles are congruent, and the Alternate Interior Angles Theorem, which states that alternate interior angles formed by a transversal and two parallel lines are congruent.

5. Can I assume that angles DEB and EBC are equal based on a diagram?

No, you cannot assume that angles DEB and EBC are equal based on a diagram alone. You must provide a proof, using mathematical properties or postulates, to show that the angles are indeed equal.

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