Question

In the adjoining figure, `squareABCD and squareAPQR` are two parallelograms. Prove that :
`angleC=angleQand angleB=angleR`

Answer 1

`squareAPQR` is a parallelogram
`therefore" "angleA=angleQ("opposite" angles"are equal")...(1)`
`squareABCD` is a parallclogram
`therefore" "angleA=angleC" "("opposite"angles "are equal")" "...(2)`
From (1) and (2)
`angleC=angleQ" "...(3)`
Again, `squareABCD` is a parallelogram
`therefore" "angleB+angleC=180^(@)" "("sum of co-interior angles")`
`implies" "angleC=180^(@)-angleB" "...(4)`
and `squareAPQR` is a parallelogram
`therefore" "angleQ+angleR=180^(@)" "("sum of co-interior angles")`
`implies" "angleQ+=180^(@)-angleR" "...(5)`
From (3), (4) and (5), we get
`180^(@)-angleR=180^(@)-angleB`
`implies" "angleB=angleR`
`therefore" "angleC=angleQand angleB=angleR`