Question

Construct an isosceles triangle whose base is 8cm and altitude is 4cm and then draw another triangle whose sides are 3/2 yes the corresponding sides of the triangle.

Answer 1

See image in diagram ....

Step of Construction : --------

• Draw a line segment BC = 8 cm.
• Draw a perpendicular bisector AD (4 cm) of BC.
• Joining AB and AC we get isosceles ΔABC.
• Construct an acute ∠CBX downwards.
• Along BX mark off 3 equal points B1, B2, B3 such that BB1 = B1B2 = B2B3.
• Join C to B2 and draw a line through B3 parallel to B2C intersecting the extended line segment BC at C’.
• Again draw a parallel line C’ A’ to AC cutting BP at A’.
• ΔA ‘BC’ is the required triangle.

C’A’ || CA [By construction]

ΔABC ~ ΔA 'BC' (By AA similarity)