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Class-8 Trapezium

Introduction to Trapezium

Properties of Trapezium

Isosceles Trapezium

Properties of Isosceles Trapezium

Trapezium MCQ

Trapezium Worksheets

Answer Sheet

Introduction to Trapezium

A quadrilateral in which one pair of opposite sides is parallel is known as trapezium.

Class 8 Trapezium

In the above figure, ABCD is a quadrilateral in which AB || CD. Hence ABCD is a trapezium. Here AD and BC are not parallel to each other and known as oblique sides

Properties of Trapezium

  1. One pair of opposite sides is parallel to each other
  2. Two pair of adjacent angles are supplementary, i.e., ∠A + ∠D = 180° and ∠B + ∠C = 180°

Isosceles Trapezium

If the two non-parallel sides of a trapezium are equal, then it is known as isosceles trapezium.

Class 8 Trapezium

Properties of an Isosceles Trapezium

In an isosceles trapezium ABCD,
Class 8 Trapezium

  1. One pair of opposite sides is parallel i.e., AB || CD.
  2. Two pair of adjacent angles are supplementary, i.e., ∠A + ∠D = 180° and ∠B + ∠C = 180°.
  3. Angles on the same base are equal, i.e., ∠A = ∠B and ∠C = ∠D.
  4. Diagonals are equal in length, i.e., AC = BD.

Example 1. Find the perimeter of the below given isosceles trapezium.
Class 8 Trapezium
Solution. In an isosceles trapezium two non-parallel sides are equal i.e., AD = BC = 4 cm

Perimeter of the ABCD isosceles trapezium = AB + BC + CD + AD

       = 7 cm + 4 cm + 5 cm + 4 cm

       = 20 cm.

Hence, perimeter of ABCD isosceles trapezium is 20 cm.

Example 2. ABCD is an isosceles trapezium, find the value of ∠A and ∠C.
Class 8 Trapezium
Solution. Isosceles trapezium angles on the same base are equal, i.e., ∠A = ∠B = 70° and ∠C = ∠D = 110°.

Hence, ∠A = 70° and ∠C = 110°.

Example 3. ABCD is an isosceles trapezium, find the value of ∠B, ∠C and ∠D.
Class 8 Trapezium
Solution. In an isosceles trapezium two pair of adjacent angles are supplementary, i.e., ∠A + ∠D = 180° and ∠B + ∠C = 180°.

∠A + ∠D = 180°

=> 75° + ∠D = 180°

=> ∠D = 180° − 75°

=> ∠D = 105°

As we know isosceles trapezium angles on the same base are equal, i.e., ∠A = ∠B and ∠C = ∠D.

∠A = ∠B = 75°      ∠C = ∠D = 105°

Hence, ∠B = 75°

Example 4. Find the value of p in the below given trapezium ABCD.
Class 8 Trapezium
Solution. In the given ABCD trapezium ∠A = (p − 20)° and ∠D = (p + 40)°.

As we know, in a trapezium, the angles on either sides of the base are supplementary.

∠A + ∠D = 180°

=> (p − 20) + (p + 40) = 180

=> 2p + 20 = 180

=> 2p = 180 − 20

=> 2p = 160

=> p = 1602

=> p = 80

Hence, the value of p is equal to 80.

Example 5. ABCD is a trapezium such that AB || CD, ∠A : ∠D = 2 : 1 and ∠B : ∠C = 7 : 5. Find the measure of all the angles of the trapezium.
Class 8 Trapezium
Solution. Let's assume ∠A = 2p and ∠D = p.

As we know ∠A and ∠D are supplementary.

∠A + ∠D = 180°

=> 2p + p = 180°

=> 3p = 180°

=> p = 180°3

=> p = 60°

∠A = 2p = 2 × 60° = 120°

∠D = 60°

Let's assume ∠B = 7q and ∠C = 5q are supplementary.

Similarly, ∠B and ∠C are supplementary.

∠B + ∠C = 180°

=> 7q + 5q = 180°

=> 12q = 180°

=> q = 180°12

=> q = 15°

∠B = 7q = 7 × 15° = 105°

∠C = 5q = 5 × 15° = 75°

Hence, ∠A = 120°, ∠B = 105°, ∠C = 75° and ∠D = 60°.

Example 6. In trapezium ABCD, DO and CO are bisectors of ∠D and ∠C respectively. Find ∠A and ∠B.
Class 8 Trapezium
Solution. ∠ODC = ∠ODA = 30° and ∠OCD = ∠OCB = 30°

So, ∠D = 60° and ∠C = 60°.

Since, ABCD is a trapezium,

∠A + ∠D = 180° and ∠B + ∠C = 180°

=> ∠A + 60° = 180°    => ∠B + 60° = 180°

=> ∠A = 180° − 60°    => ∠B = 180° − 60°

=> ∠A = 120°    => ∠B = 120°

Hence, ∠A = 120° and ∠B = 120°.

Class-8 Trapezium MCQ

Trapezium Test - 1

Trapezium Test - 2

Class-8 Trapezium Worksheets

Trapezium Worksheet - 1

Trapezium Worksheet - 2

Answer Sheet

Trapezium-AnswerDownload the pdf










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