Construct a triangle PQR in which angle P=60 degree, angle Q = 45 degree and perimeter of triangle PQR is 15 cm.
Answers
Step-by-step explanation:
third angle of the triangle will be 105 degree
- draw a line of 6cm
- Mark angle p on one end(60 degree) with measure 4cm.
- Mark angle q on the other end(45 degree)with measure 5cm
- join
1) Draw a line BC of length 15 cm
2) At B draw 60 degrees
3) At C draw an angle of 45 degrees(90 deg and then bisect it)
4) Bisect these two angles to get 30 and 22.5 degrees and the meeting point of these two lines is P so <PBC=30 deg and <PCB=22.5 degrees
5) Now perpendicular bisect PB and PC such that when extended they intersect BC at Q and R and PB and PC at X and Y respectively
6) Join PQ and PR we have the triangle.
Proof:
Triangle PXQ and BXQ are congruent because XQ is common, PX = BX and <PXQ = < BXQ=90 degrees
So BQ = PQ and <XBQ = <XPQ = 30 degrees
Thus <PQR=<XBQ+<XPQ=60 degrees
Similarly PYR and BYR are congruent YR is common PY = BY and <PYR = <BYR = 90 degrees
So CR = PR and <YCR = <YPR = 22.5
Thus < PRQ = <YCR + <YPR = 45 degrees
PR + PQ + QR = CR + BQ + QR