Question

Using a pair of compasses and ruler only,construct triangle XYZ,where YZ=8cm,angle XYZ=60 degrees and angle XZY=45 degrees.measure xy.

construct the locus:
a. 1 of points equidistant from yx and yz
b. 2 of point equidistant from y and z
label the point of intersection Q of locus 1 and locus 2

Answer 1

To construct triangle XYZ, measure and draw the angles at X and Z and draw line segments XY and XZ. To construct the locus of points equidistant from YX and YZ or Y and Z, use a compass to draw intersecting circles. The intersection point is labeled Q.

Step-by-step explanation:

To construct triangle XYZ, first draw a line segment YZ with a length of 8cm. Using a protractor, measure and mark a 60-degree angle at point X. Then, measure and mark a 45-degree angle at point Z. The intersection of these two angles will be point Y. Finally, draw line segments XY and XZ to complete the triangle. To measure the length of XY, use a ruler to measure the distance between points X and Y.

a. To construct the locus of points equidistant from YX and YZ, use a compass to draw circles with centers at points X and Z, both with the same radius. The intersection of these two circles will form the locus.

b. To construct the locus of points equidistant from Y and Z, use a compass to draw two circles with centers at points Y and Z, both with the same radius. The intersection of these two circles will form the locus. Label the point of intersection as Q.