question_answer

Draw an isosceles  in which  and altitude . Then construct another triangle whose sides are  of the corresponding sides of .

Answer:

Steps of construction:

(i) Draw a line segment .

(ii) Draw a perpendicular bisector of BC intersecting

BC at L such that .

(iii) Join AB and AC

Thus,  is obtained.

(iv) Below BC, make an acute angle ,

(v) Along BX, mark off four points  such that .

(vi) Join .

(vii) From  draw , meeting BC at D.

(viii) From D, draw , meeting AB at E

Then is the required triangle each of whose sides is  of the corresponding side of .