Trapezoid is quadrilateral with couple of non parallel surface and additional two surfaces are parallel. The base is the parallel side of a trapezoid. If two sides which are not parallel to every further contain equivalent lengths, then trapezoid is called an isosceles trapezoid. Base angles in this trapezoid are equal in dimension.
Let PQRS be a trapezoid with parallel sides PQ and RS is called an isosceles trapezoid if it is a strict trapezoid with QR = SP. Observe that if PQRS is a parallelogram, it is a (non-strict) trapezoid with QR = SP.
Sum of interior angle of any polygon = (n - 2) *180°.
Here isosceles trapezoid has four sides
So interior angle = (4 - 2)*180degree = 360°.
Exterior angle of any quadrilateral is 360°
So the exterior angle of isosceles trapezoid is 360°.
Base Angles:
The base angles are congruent for an isosceles trapezoid.
`/_`QPS = `/_`RSP
`/_`PQR= `/_`SRQ
Line of symmetry of Isosceles Trapezium:
One is the line of symmetry of isosceles trapezium because these angles are equal.
Characterization of isosceles trapezoids
Example1:
What is the measure of `/_`PSR , if the `/_`QPS is 45 °,?
Solution:
`/_` PSR is 45° since base angles are congruent
Example 2:
What other angle measures 120°, if `/_`PQR = 120°?
Solution:
The adjacent angle for `/_`PQR is `/_`QRS
So `/_`QRS measures 120°.