Question

Gautam had two sticks of equal length. He named them AB and CD. He then placed these two sticks in three different ways and joined their four vertices as shown below.

1. What type of quadrilateral is in:
   1. Fig. (i)?
   2. Fig. (ii)?
   3. Fig. (iii)?
2. What is the sum of consecutive angles in Fig. (iii)?
3. If ∠BAD = 70° in Fig. (iii), then what is the measure of ∠CDA?

Answer 1

1. 1. Fig. (i): Rectangle (The diagonals are equal in length and bisect each other).
   2. Fig. (ii): Rhombus (The diagonals bisect each other at right angles).
   3. Fig. (iii): Parallelogram (The diagonals bisect each other, but are not necessarily equal or perpendicular)
2. The sum of consecutive (co-interior) angles in any parallelogram is 180°.
3. Since consecutive angles in a parallelogram are supplementary:
   ∠BAD + ∠CDA = 180°
   70° + ∠CDA = 180°
   ∠CDA = 180° − 70° = 110°