Diagonals of a Rhombus Bisect Each-Other at Right Angles
Question 7 ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.
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Let us join AC. In ∠ ABC, BC=AB (Sides of a rhombus are equal to each other) ∠1=∠2 ( Angles opposite to equal sides of a triangle are equal) However, ∠1=∠3 (Alternate interior angles for parallel lines AB and CD) ∠2=∠3 Therefore, AC bisects ∠C. Also, ∠2=∠4 ( Alternate interior angles) ∠1=∠4 Therefore, AC bisects ∠A Similarly, it can be proved that BD bisects ∠ B and ∠ D as well.