Since we know that ABCD is an isosceles trapezoid, the value of Option C. x= 17
we can also assume that its diagonals have the same length, which means:
AC = BD
=> 7x - 21 = 5x + 13
=> 7x - 5x = 21 + 13
=> 2x = 34
=> x = 34/2 = 17
So the answer is C.
An isosceles trapezoid is a trapezoid with congruent base angles and congruent non-parallel sides. A trapezoid is a quadrilateral with only one of its sides parallel. An isosceles trapezoid has many interesting properties that make it unique and help us differentiate it from the other quadrilaterals
Properties of Isosceles Trapezoid
- It has an axis of symmetry. It has no rotational symmetry and one line of symmetry joining the midpoint of the parallel sides.
- One pair of sides is parallel and they are the base sides. (AB II DC in the given image)
- The remaining sides other than the base are non-parallel and are equal in length. (c = d in the given image)
- The diagonals are the same in length. (AC = BD)
- The base angles are the same. (∠D = ∠C, ∠A=∠B)
- The sum of opposite angles is 180° or supplementary. (∠A + ∠C = 180° and ∠B + ∠D = 180°)
- The line segment joining the midpoints of the parallel sides is perpendicular to the bases. (PQ ⊥ DC)
Learn more about Isosceles Trapezoid, refer
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