Question

Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are $1{\displaystyle \frac{1}{2}}$ times the corresponding sides of the isosceles triangle.

Answer 1

Hint: Here we will construct the triangle by step by step procedure. An isosceles triangle has 2 sides of equal length.

Complete step-by-step answer:

Steps of Construction:
1.Draw a base BC of length 8 cm.
2.Draw the perpendicular bisector of BC and name it PQ. Let it intersect BC in M.
3.From M, mark an arc A at a distance of 4 cm (given altitude of triangle) on PQ.
4.Join BA and CA. $△ABC$ is the first isosceles triangle.
5.Extend BC and BA. Place the pointed end of the compass at C and mark an arc of radius of CM on the opposite side of M on the extended segment BC. Mark the point as D (since CM is half of BC,BD will be BC+0.5BC=1.5BC)
6.From D, draw a line parallel to AC and let it intersect the extended segment AB at E.
$△FED$ is the required similar triangle.

Note: In this type of questions construct the triangle carefully, and follow step by step procedure.