(I) Construct an isosceles triangle XYZ such that XY= YZ = 8 cm and XYZ = 60 degrees
(ii) Construct the bisector of angle Y
(iii) Construct the perpendicular bisector of side XY.
details of these constructions can easily be found online.
For example, a 60° angle can be constructed as follows
construct line segment XY of length 8
Use XY as the radius of a circle with center at X
Use XY as the radius of a circle with center at Y
Where the two circles intersect is point Z.
angle XYZ is 60°, and XY=YZ.
I don, t know
(i) To construct an isosceles triangle XYZ with XY = YZ = 8 cm and XYZ = 60 degrees, follow these steps:
1. Draw a line segment XY of length 8 cm.
2. Place the compass on point X and draw an arc with a radius of 8 cm to intersect the line XY. Label this point as A.
3. Place the compass on point Y and draw an arc with a radius of 8 cm to intersect the line XY. Label this point as B.
Now, we have X, Y, and A as the vertices of the triangle.
4. Place the compass on point Y and draw an arc with a radius larger than XY to intersect the previously drawn arc centered at A. Label this point as Z.
Now, we have X, Y, and Z as the vertices of the isosceles triangle XYZ.
(ii) To construct the bisector of angle Y, follow these steps:
1. Draw a ray from point Y in any direction.
2. Place the compass on point Y and draw an arc that intersects both sides of angle Y.
3. Without changing the compass width, place the compass on the points where the arcs intersect the sides of angle Y and draw two arcs that intersect each other inside the angle. Label the points of intersection as C and D.
4. Draw a line segment CD to connect points C and D.
Now, CD is the bisector of angle Y.
(iii) To construct the perpendicular bisector of side XY, follow these steps:
1. Draw a line segment XY.
2. Place the compass on point X and set the compass width to more than half of XY.
3. Draw arcs from both ends of XY intersecting each other. Label the points of intersection as A and B.
4. Place the compass on point B and set the compass width to more than half of XY.
5. Draw an arc from point B intersecting the previously drawn arc centered at point A (or vice versa).
6. Draw a line segment AB through the points of intersection.
Now, AB is the perpendicular bisector of side XY.