Question

Construct a triangle PQR, in which $\angle$P = 30°, $\angle$Q = 45° and PQ + QR + RP = 22 cm. [4 MARKS]

Answer 1

Steps : 1 Mark
Construction : 3 Marks

Steps :
1.Draw line segment BC of length 22 cm.
2. From B draw ray BL which makes angle 30 degree with BC using protractor.
3. Similarly draw ray CM which makes angle 90 degrees with BC.
4. Using angle bisector construction method, draw angle bisectors for $\angle LBC$ and $\angle MCB$. Let these 2 angle bisectors meet at R.
5. Using perpendicular bisector construction method draw perpendicular bisectors DE for BR and FG for CR respectively.
6. Let the point where DE meets BC be P and let the point where FG meets BC be Q. Join RP and RQ.
7. $\Delta PQR$ is the required triangle.