State true of false. Give reason also.
By geometrical construction, it is possible to divide a line segment in the ratio 3+root 2 : 3-root 2 .
Yes, it is possible to divide a line segment in the ratio by geometrical construction.
Steps of construction are given below.
Step 1: Draw a line segment AB.
Step 2: Draw any ray AD, making an acute angle ∠BAD with AB.
Step 3: Along AD, mark off point A1, A2, A3, A4, A5, A6 such that AA1 = A1A2 = A2A3 = A3A4 = A4A5 = A5A6 = 1 units
Step 4: Join BA6.
Step 5: Draw A4C ⊥ AD at A4 such that A4C = 1 unit.
Step 6 : Join A3C.
Step 7: With A3 as centre and radius = A3C draw an arc intersecting AD in X.
Step 8: Draw XY || A6B, intersecting AB in Y.
Here, Y divides AB in the ratio .
ΔAXY ∼ ΔABA6 (AA similarity)