Construct an isosceles triangle whose base is 9 cm and altitude 5 cm. Construct another triangle whose sides are 3/4 of the corresponding sides of the first isosceles triangle.

Question

Philoid · Accepted Answer

Steps of Construction:

1. Draw a line segment AB of length 9 cm.

2. Now as we know that the altitude of the isosceles triangle is also the bisector of the base line. So we draw a perpendicular bisector of line BC.

3. We cut an arc of length 5 cm( length of altitude). The arc cut point is C.

4. Join AB and AC. ABC is the triangle of the given dimensions.

5. Now we have draw a triangle which is 3/4 times of this triangle.

6. Draw a ray from A making an acute angle with AB. Make 4 equal arcs along the ray, i. e. A1, A2, A3, and A4.

7. Join A4B.

8. From A3, draw a line parallel to A4B cutting AB at B’.

9. From B’, draw another line parallel to BC cutting AC at C’.

10. AB’C’ is our required triangle.