Let us prove that the two adjacent angles of any parallel side of a trapezium are equal.
Answers
Answer:
It is only with isosceles trapezium and not the other kind.
Draw the isosceles trapezium and name them ABCD, AB (longer side) being parallel to CD (shorter side).
Extend AD and BC to meet at P. Now triangles PAB and PDC are similar and both are isosceles. Also PA = PB being isosceles triangles as also PD = PC.
<PAB =<PBA = <PDC = <PCD.
The supplementary angles of <PDC which is <CDA and of <PCD, which is <DCB are also equal.
Hence the two adjacent angles of the two parallel sides of an isosceles trapezium are equal.
Answer:
It is only with isosceles trapezium and not the other kind.
Draw the isosceles trapezium and name them ABCD, AB (longer side) being parallel to CD (shorter side).
Extend AD and BC to meet at P. Now triangles PAB and PDC are similar and both are isosceles. Also PA = PB being isosceles triangles as also PD = PC.
<PAB =<PBA = <PDC = <PCD.
The supplementary angles of <PDC which is <CDA and of <PCD, which is <DCB are also equal.
Hence the two adjacent angles of the two parallel sides of an isosceles trapezium are equal.
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It depends a bit on your nationality.
If you’re British, you mostly don’t.
And if you’re not, you usually can’t.
The reason is that there are two definitions for trapezium - one involves parallel sides, and the other doesn’t.
The other reason is that even if there is a pair of parallel sides, the angles are not equal. The only time the angles will be equal is if the parallel sides share a common centre. Or the line joining the two parallel sides is perpendicular to those sides.
The easiest proof was created by a computer program designed to solve geometric problems. It is believed that this solutio
If two angles of a trapezium are given, what is the measurement of their opposite angles?
If two angles of a trapezium are given what is the measure of their opposite angles.
Whether this question can be solved or not depends on which are the two angles given.