Mathematics
Prashant had a plot of land in the shape of a quadrilateral. He constructed his house in the middle by joining the mid-points of the four sides of the land and used the remaining four portions at the four ends for different purposes, like a small garden, swimming pool, etc.
(i) What type of a quadrilateral is PQRS ?
(ii) What are the lengths of adjacent sides of the quadrilateral PQRS, if their ratio is 1 : 2 and the perimeter of the quadrilateral is 180 m ?
(iii) In quadrilateral PQRS, if ∠PSQ = 30° and ∠QRS = 110°, find ∠SQP.
Related Questions
In the following figure, ABCD is a rhombus and DCFE is a square.
If ∠ABC = 56°, find :
(i) ∠DAE
(ii) ∠FEA
(iii) ∠EAC
(iv) ∠AEC
In parallelogram ABCD, E is the mid-point of side AB and CE bisects angle BCD. Prove that :
(i) AE = AD
(ii) DE bisects angle ADC
(iii) angle DEC is a right angle
In parallelogram ABCD, X and Y are mid-points of opposite sides AB and DC respectively. Prove that :
(i) AX = YC
(ii) AX is parallel to YC
(iii) AXCY is a parallelogram
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.
(i) What type of quadrilateral is in :
(a) Fig (i) ?
(b) Fig (ii) ?
(c) Fig (iii) ?
(ii) What is the sum of consecutive angles in Fig (iii) ?
(iii) If ∠BAD = 70° in Fig (iii), then what is the measure of ∠CDA ?