Use a ruler and a pair of compasses only in this question
a)Construct a triangle PQR such that PQ=6.0cm,Angle PQR=30° and PR=8cm
b)Locate a point such that
I)S and Q are on either side of PR
ii)QS=8cm
iii)PS=SR
c)i) Construct a line through R and parallel to QS to intersect line PQ produced at T
ii)Measure TR
a) To construct triangle PQR, follow these steps:
1. Draw a line segment PQ of length 6.0cm using a ruler.
2. Place the compass at point P and draw an arc with a radius of 8cm, intersecting PQ at point S.
3. Without changing the compass width, place the compass on point S and draw another arc intersecting the previous arc at point R.
4. Draw a line segment PR connecting points P and R.
You have now constructed triangle PQR.
b) To locate a point satisfying the given conditions, follow these steps:
1. Draw a line segment PR of length 8cm using a ruler.
2. Place the compass at point P and draw an arc with a radius of 8cm, intersecting PR at point S.
3. Without changing the compass width, place the compass on point S and draw another arc intersecting PR at point T.
4. This will locate a point T satisfying the conditions.
c) To construct a line through R parallel to QS, follow these steps:
1. Place your ruler on point R and angle it so that it passes through point Q.
2. Draw a line segment through point R, extending it towards point Q, while keeping the ruler parallel to QS.
3. This line will be parallel to QS and pass through R.
To measure TR, follow these steps:
1. Place your ruler on point T and extend it towards R.
2. Measure the length from T to the intersection point with the line you drew in part c(i).
3. This measurement is the length of TR.