Deduction 7 - What can we say about the sides of a parallelogram?

Transcript

Deduction 7 What can we say about the sides of a parallelogram?We need to find relation between sides of Parallelogram To do this, we consider a Parallelogram ABCD To check sides, we use congruency We prove triangles ∆ ADB & ∆ CBD congruent Since ABCD is a parallelogram Opposite angles are equal ∴ ∠ A = ∠ C Opposite sides of Parallelogram are parallel So, AD & BC are parallel And, BD is a transversal Since Alternate Angles are equal ∴ ∠ ADB = ∠ CBD In ∆ ADB and ∆ CBD ∠ A = ∠ C ∠ ADB = ∠ CBD BD = BD ∴ ∆ ADB ≅ ∆ CBD By CPCT (Corresponding Parts of Congruent Triangles) AB = CD Similarly, we can prove AD = BC Thus, in parallelogram ABCD, Both pairs of Opposite sides is equal