Question

Construct an isosceles triangle whose base is 6 cm and altitude is 3cm and then another triangle whose sides are 3/2 times the corresponding sides of the isosceles triangle.

Answer 1

1. Mark a point B that will be one vertex of the new triangle.

2. Set the compasses' width to 6 cm, the length of the segment BC.

3. With the compasses' point on B, make an arc near the future vertex C of the triangle.

4. Mark a point C on this arc. This will become the next vertex of the new triangle. Join B and C.

5. To ocnstruct the perpendicular bisector of BC, place the compasses on one end of the line segment. Set the compasses' width to a approximately two thirds the line length. The actual width does not matter.

6. Without changing the compasses' width, draw an arc above and below the line.

7. Again without changing the compasses' width, place the compasses' point on the the other end of the line. Draw an arc above and below the line so that the arcs cross the first two.

8. Using a straightedge, draw a line between the points where the arcs intersect. This line is perpendicular to the first line and bisects it.

9. Set the compasses' width to the distance from A to B. This is the desired altitude of the triangle = 3 cm.

10. Place the point of the compasses on the midpoint of the base line, and draw an arc across the perpendicular drawn earlier. This is the third vertex A, of the triangle.

11. Draw the two side lines AB and AC. This is an isosceles triangle ABC.

Answer 2

Answer:

Let ABC be an isosceles triangle with AB = AC, base BC = 6 cm and altitude AD = 4 cm.

A ΔA'BC', whose sides are 34 times the sides of ΔABC, can be drawn using the following steps:

1. Draw a line segment BC of 6 cm. Draw arcs of the same radius on both sides of the line segment while taking points B and C as its centre. Let these arcs intersect each other at O and O'. Join OO'. Let OO' intersect BC at D

2. Taking D as centre, draw an arc of 4 cm radius which cuts the line segment OO' at point A. An isosceles ΔABC is formed, having altitude (AD) as 4 cm and base (BC) as 6 cm.

3. Draw a ray BX making an acute angle with line segment BC on the opposite side of