Using a ruler and a pair of compasses only, construct (i) a triangle EFG, such that ǀFGǀ = 7.5cm, ˂EFG = 120o and ˂EGF= 22.5o, measure EG. (ii) The locus L1 of point equidistant from F and G (iii) The locus L2 of points 5cm from F. (b) Measure H1 H2 where H1 and H2 are points of intersection of L1 and L2?

LawsonOche

3 years ago

To construct the triangle EFG and find the measurements you mentioned, follow these steps:

(i) Constructing triangle EFG:

1. Draw a line segment FG of length 7.5 cm using a ruler.
2. Place the compass at point F and draw an arc with a radius of 7.5 cm, intersecting FG at point P.
3. Without changing the compass width, place the compass at point G and draw an arc that intersects the previous arc at point Q.
4. Join points F and Q with a straight line segment to form the side FQ of triangle EFG.
5. Set the compass width to a distance of EG.
6. Place the compass at point F and draw an arc that intersects FQ at point R.
7. Without changing the compass width, place the compass at point G and draw an arc that intersects FQ at point S.
8. Join points R and S with a straight line segment to form the remaining sides of triangle EFG.

(ii) Finding the locus L1:

1. With the compass width set at any length, place the compass at point F and draw an arc.
2. Without changing the compass width, place the compass at point G and draw another arc.
3. These arcs will intersect at two points. Join these points with a straight line.
4. This line represents the locus L1, which consists of all points equidistant from F and G.

(iii) Finding the locus L2:

1. With the compass width set to 5 cm, place the compass at point F and draw an arc.
2. This arc represents the locus L2, which consists of all points that are 5 cm away from F.

(b) Measuring H1H2:

1. The points of intersection between L1 and L2 are H1 and H2.
2. Use a ruler to measure the distance between H1 and H2. This measurement represents the length H1H2.