Constuct triangle XYZ such that |XY|=8cm, angle YXZ =105° and angle XZY =45°
The classical definition of "construct" in geometry restricts your tool to
only a straightedge and a compass.
Since your are required to measure XY to be 8 cm, we are simply going
to draw it.
Start with a base of XY and measure it off at 8 cm/
Using a protractor, at X, measure an angle of 105°and draw a ray from X
at Y measure an angle of 30° and draw a ray from Y,
(you know 2 of the angles, so the missing angle = 180-105-45 = 30 )
Mark Z, the intersection of the rays.
That's it, your are done
If you don't have a protractor, it is easy to construct the 105° angle, since 105=90+15
So just make a 90° angle
make a 60° angle and bisect it twice to get the 15° angle
Then add them together.
To construct triangle XYZ with the given conditions, follow these steps:
1. Start by drawing a straight line segment XY of length 8 cm.
2. At point X, use a protractor to draw an angle of 105 degrees. Place the protractor such that one side is aligned with line XY, and the center of the protractor is at point X. Mark the intersection of the protractor's other side with line XY as point Z.
3. From point Z, draw another angle of 45 degrees. Again, place the protractor such that one side is aligned with line XZ, and the center is at point Z. Mark the intersection of the protractor's other side with line XZ as point Y.
4. Finally, draw line segment YZ to complete the triangle XYZ.
Ensure that you measure and mark the given angles accurately to get an accurate construction of the triangle.