Q. 165.0( 2 Votes )

# Construct an isos

Answer :

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.

As And 3 is greater between 3 and 2,

So

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 Awhich 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.

Justification:

We need to prove, By construction 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,

Hence, Rate this question :

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