Question 9 - Figure it out - Page 107 - Chapter 4 Class 8 - Quadrilaterals (Ganita Prakash)

Transcript

Question 9 What type of a quadrilateral is one in which the opposite sides are equal? Justify your answer. Hint: Draw a diagonal and check for congruent triangles.Let’s consider a quadrilateral ABCD We need to check if sides are parallel So, we try to check if ∠ ADB = ∠ CBD To do this, we try to prove triangles ∆ AOE & ∆ YOS congruent In ∆ ADB & ∆ CBD AD = CB AB = CD DB = DB ∴ ∆ ADB ≅ ∆ CBD By CPCT (Corresponding Parts of Congruent Triangles) ∠ ADB = ∠CBD For lines AD and BC With transversal BD ∠ ADB = ∠ CBD Since alternate angles are equal ∴ AD ∥ BC Similarly, we can prove AB ∥ CD Thus, in ABCD Opposite sides are equal and parallel ∴ ABCD is a parallelogram