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In this section ,we will discuss some trapezoid and its theorems.Trapezoid is a quadrilateral with at least one pair of parallel sides. AB || CD. (if there are two pairs of parallel lines then it is a parallelogram)When non-parallel sides in trapezoid are equal then it is know ans isosceles trapezoid.Theorem 1: A trapezoid is isosceles if and only if the base angles are congruent.Given : ABCD is an isosceles trapezoid. AD = BC and AB || CD.Prove that : ∠C = ∠D
Example : In a trapezoid PQRS, PQ||RS and PS = QR. If ∠S = 600 then find the remaining angles.Solution :PQ||RS and PS = QR, so trapezoid PQRS is an isosceles trapezoid.In isosceles trapezoid, base angles are equal.(trapezoid and its theorems)∠S = ∠R and ∠P = ∠QBut ∠S = 600∴ ∠R = 600Let ∠P = ∠Q = xSum of all the angles in a quadrilateral is 360.∴ ∠P + ∠Q + ∠S + ∠R = 360x + x + 60 + 60 = 3602x +120 = 3602x = 360 -1202x = 240∴ x = 240/2x = 120∠P = ∠Q = 1200__________________________________________________________________Some important theorems of trapezoids are given below :
Practice1) In a trapezoid ABCD,AB|| CD and BC = AD. If m∠C=650 then find m∠D.2) PQRS is a trapezium in which PQ || RS. If ∠P = ∠Q = 40, find the measures of other two angles.3) In trapezoid ABCD, ∠B= 1200 Find m∠C.4) In a quadrilateral HELP, if EP = LH then what type of quadrilateral it is?5) In a quadrilateral, the angles are in the ratio of 4:5:3:6.Find the measures of each angles.6) If three angles in the trapezoid are 1300,1200,500 and 2×0. Find x and the 4th angle.7) Draw a isosceles trapezoid named PQRS, PS||QR and PQ = SR.Quadrilateral• Introduction to Quadrilateral• Types of Quadrilateral• Properties of Quadrilateral• Parallelogram and its Theorems• Rectangle and its Theorems• Square and its Theorems• Rhombus and its Theorems• Trapezoid and its Theorems• Kite and its Theorems• Mid Point TheoremGeometryHome Page
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