Construct a triangle xyz in which xy=8cm, angle xyz=60° angle yxz=90°. A perpendicular bisector of xy and let it cut xy at p. Measure and state the length of pq
How can
A perpendicular bisector of xy cut xy ?
And where is q?
Try again.
But I will say that the perpendicular bisector of xy also bisects yz.
Show using similar triangles
To construct triangle XYZ, we will follow the given conditions step by step.
Step 1: Draw a line segment XY of length 8cm. This will be one side of the triangle.
Step 2: From point X, draw a ray forming an angle of 60 degrees with line XY. This will be the second side of the triangle, XZ.
Step 3: From point Y, draw another ray forming a right angle (90 degrees) with line XY. This will be the third side of the triangle, YZ.
Triangle XYZ is now constructed according to the given conditions.
Next, we are asked to construct a perpendicular bisector of XY and find the length of PQ, where PQ is the intersection of the perpendicular bisector and line XY.
To construct the perpendicular bisector:
Step 4: From point X, draw an arc on both sides of line XY. This arc should be large enough to intersect with ray YX.
Step 5: From point Y, draw a similar arc on both sides of line XY, intersecting with ray XY.
Step 6: Connect the intersection points of the arcs on both sides using a straight line. This line will be the perpendicular bisector of XY.
Let the intersection of the perpendicular bisector and line XY be point P.
To measure and find the length of PQ:
Step 7: From point P, draw a line perpendicular to line XY, intersecting with line YX. Let the intersection point be Q.
Step 8: Measure the distance between points P and Q. This will give you the length of PQ, which is the answer to the question.
By following these construction steps, you will be able to construct triangle XYZ and measure the length of PQ.