Using a ruler and a pair of compass only.
a.constructa triangle ABC such that angle ABC is 90°,BA is 10cm and angle BAC is 30°. Measure BC.
b.) i bisect the angle ACB to meet BC at D.
ii what type of traingle is CDA.
a. To construct triangle ABC:
1. Draw a line segment, AB, of length 10 cm using the ruler.
2. Place the compass tip at point A and draw an arc with a radius of 10 cm above and below point B on line AB.
3. Without changing the compass width, place the compass tip at point B and draw two more arcs intersecting the previous arcs.
4. Label the points where the intersecting arcs meet as points C and D.
5. Draw a line segment, AC, connecting point A to point C using the ruler.
b. To bisect angle ACB and find point D:
1. Place the compass tip at point C, and draw an arc that intersects line segment AC on both sides.
2. Without changing the compass width, place the compass tip at point B and draw an arc that intersects the previous arc at two points (label one of these points as D).
3. Draw a line segment, CD, connecting points C and D using the ruler.
ii. Triangle CDA is an isosceles triangle because line segments CD and CA are equal in length.
a. To construct triangle ABC, follow these steps:
1. Draw a line segment AB of length 10 cm using a ruler.
2. Place the compass point on point B and draw an arc in the direction of point A.
3. Without changing the compass width, place the compass point on point A and draw an arc that intersects the previous arc at point C.
4. Draw a line segment BC connecting points B and C using a ruler.
5. To find the measurement of BC, measure the length of the line segment BC using the ruler.
b. To bisect angle ACB, follow these steps:
1. Place the compass point on point C and draw an arc that intersects AB at two points, let's call them E and F.
2. Without changing the compass width, place the compass point on point E and draw an arc that intersects the previous arc at point G.
3. Without changing the compass width, place the compass point on point F and draw an arc that intersects the arc drawn from point E at point H.
4. Draw a line segment GH connecting points G and H using a ruler.
5. The line segment GH will bisect angle ACB at point D.
ii. Based on the construction, triangle CDA is an isosceles triangle.