Isosceles Trapezoid Angle

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.

 

isosceles trapezoid angle

 

Angles of an Isosceles Trapezoid:

isosceles trapezoid anglec

   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:

isosceles trapezoid anglex

The base angles are congruent for an isosceles trapezoid.

     `/_`QPS = `/_`RSP

     `/_`PQR= `/_`SRQ

 

Line of symmetry of Isosceles Trapezium:

 isosceles trapezoid angle1

One is the line of symmetry of isosceles trapezium because these angles are equal.

 

Characterization of isosceles trapezoids

  • Base angles of an isosceles trapezoid are equivalent.
  • Diagonals of an isosceles trapezoid are equivalent
  • Opposite angles are auxiliary.
  • The addition of two adjacent angles are equivalent to 180°
  • An isosceles trapezoid with a particular angle and diagonal.
  • The addition of all the interior angles are equal to 360°
  • The center of a trapezoid is a segment, it connects the midpoints of the nonparallel surface.
  • It has similar bases. Its extent equals half the addition of the base lengths.
  • The angles on any surface of the bases are the similar size/measure (congruent).

 

Example Problems for Isosceles Trapezoid Angle:

 

Example1:

   What is the measure of `/_`PSR , if the `/_`QPS is 45 °,?

Solution:

isosceles trapezoid anglez 

`/_` PSR is 45° since base angles are congruent

 

Example 2: 

 

   What other angle measures 120°, if  `/_`PQR = 120°?

 

Solution:

isosceles trapezoid angleb

   The adjacent angle for `/_`PQR is `/_`QRS

   So `/_`QRS measures 120°.