using a pair of ruler and compasses only construct a quadrilateral PQRS such that /PQ/=8cm, QPS=105°,angle PQS=30°,/PR/=9cm, RS=RQ
I assume you know how to bisect an angle.
So, construct an equilateral triangle, with angles of 60°
Bisect one of those angles, and then again. That will give you angles of 30° and 15°
So.
Construct PQ of length 8
At P, construct angle of 105°
At Q, construct angle of 30°
Extend the sides of the angles to intersect at S.
Draw a circle with center at P, of radius 9.
Construct the perpendicular bisector of QS. It intersects the circle at R.
Yes
No answer
To construct a quadrilateral PQRS with the given conditions using only a pair of ruler and compasses, follow these steps:
1. Draw a line segment PQ of length 8 cm using a ruler.
2. Place the compass at point P and draw an arc with a radius of 9 cm to intersect the line segment PQ at point A. Label this point as A.
3. Without changing the compass width, place the compass at point A and draw an arc to intersect the line segment PQ at point S. Label this point as S.
4. Place the compass at point S and draw an arc with a radius equal to the length of RS (which is the same as RQ since R is the midpoint of PQ) to intersect the previously drawn arc at point R. Label this point as R.
5. Using a ruler, draw a line segment RS connecting points R and S.
6. Finally, draw a line segment QS connecting points Q and S.
You have successfully constructed the quadrilateral PQRS.