Question

Using ruler and a pair of compasses only construct

(i) triangle XYZ such that the length XY = 10 cm, angle XYZ-30° and length YZ-9 cm;
(ii) perpendicular from Z to meet line XY at P
(iii) measure the
(α) length PZ,
(β) angle XZY.
(iv) calculate, correct to the nearest whole number, the area of triangle XYZ.

Answer 1

To construct triangle XYZ, draw line segments XY and YZ with their given lengths, then connect the endpoints to form the triangle. To find the height PZ and angle XZY, use a ruler and protractor. To calculate the area of the triangle, use the formula (1/2) * base * height.

Step-by-step explanation:

To construct triangle XYZ, follow these steps:

1. Using a ruler, draw a line segment XY with a length of 10 cm.
2. Using a compass, draw an arc from point X with a radius of 9 cm to intersect line XY at point Z.
3. Draw lines from points X and Y to point Z to form triangle XYZ.

To construct a perpendicular from point Z to line XY:

1. Using a compass, draw an arc from point Z to intersect line XY at point P.
2. Draw a line from point Z to point P.

To measure the length PZ and angle XZY:

1. Use a ruler to measure the length of line PZ.
2. Use a protractor to measure the angle XZY.

To calculate the area of triangle XYZ:

1. Use the formula Area = (1/2) * base * height.
2. The base is the length XY.
3. The height can be found by dropping a perpendicular from any vertex to the opposite side and measuring its length.
4. Calculate the area using the given measurements and round to the nearest whole number.