construct a triangle ABC in which BC = 60 degree and c=45 degree and the perimeter of the triangle is 10 centimetre
Answers
Answer:
The construction of such triangle is attached with this
Step-by-step explanation:
To construct a triangle, given its perimeter and its two base angles.
Given the base angles, say ∠ B = 45° and ∠C = 45° and BC + CA + AB =10 cm
Steps of Construction
1. Draw a line segment, say XY equal to BC + CA + AB = 10 cm
2. Make angles LXY equal to 45° and MYX equal to 45°
3. Bisect ∠LXY and ∠MYX. Let these bisectors intersect at a point A
4. Draw perpendicular bisectors PQ of AX and RS of AY.
5. Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC
The justification of the construction
B lies on the perpendicular bisector PQ of AX.
Therefore, XB = AB and similarly, CY = AC.
This gives BC + CA + AB = BC + XB + CY = XY. = 10 cm
Again
∠BAX =∠AXB (As in ∆ AXB, AB = XB) and
∠ABC =∠BAX + ∠AXB = 2 ∠AXB = ∠LXY = 45°
Similarly,∠ACB =∠MYX = 45° as required.
Answer:
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Step-by-step explanation:
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