Construct triangle PQR angle P =60 Ang Q=45 perimeter 15cm
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
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