Q. 165.0( 2 Votes )
Construct an isos
Steps of construction:
i. Now in order to make a triangle, draw a line segment AB = 8 cm.
ii. Draw two arcs intersecting at 4 cm distance from points A and B; on either side of AB.
Join these arcs to get perpendicular bisector CD of AB. (Since, altitude is the perpendicular bisector of base of isosceles triangle).
iii. Join points A and B to C in order to get the triangle ABC.
iv. Now, draw a ray AX which is at an acute angle from point A.
And 3 is greater between 3 and 2,
Plot 3 points on AX such that:
AA1 = A1A2 = A2A3.
v. As 2 is smaller between 2 and 3. Join A2 to point B.
Draw a line from A3 which is parallel to A2B meeting the extension of AB at B’.
vi. Draw B’C’ || BC. Then, draw A’C’ || AC.
Triangle AB’C’ is the required triangle.
We need to prove,
As C'B' || CB
They will maker equal angles with line AB.
∠ACB = ∠AC'B' ..... (corresponding angles)
In ΔACB and ΔAC'B'
∠A = ∠A (common)
∠ACB = ∠AC'B' (corresponding angles)
So ΔACB ∼ ΔAC'B'
As corresponding sides of similar triangles are in ratio,
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