Using a ruler and a pair of compasses only (I) construct a triangle XYZ such that XY =8cm and angle YXZ =ANGLE ZYX =45 DEGREES . Locate a point P In the triangle equidistant from XY AND XZ AND YX AND YZ . Construct a circle touching the three sides of the triangle and measure it's radius
from P the radii of length r are perpendicular to xz, xy, and yz and all the same.
if draw it with your compass your see a certain symmetry
call the tangent point on xz Q and the one on xy S
triangle XQP is congruent to XSP and is a right triangle
the two angles at x are 22.5 degrees
so PQ = PS = 4 tan 22.5
Using a ruler and a pair of compasses only.
(a)construct triangle XYZ such that,|XY|=9.5cm,|YZ|=8cm=|XZ|
(i)construct the mediator of<YXZ
(ii)construct a line equidistant from X and Z.
(b)Name the the intersection of the mediator of<YXZ and line equidistant from X and Y,A.
(c)measure (i)|AX|(ii)<XZY
Yes
To construct the triangle XYZ, follow these steps:
1. Take a ruler and draw a line segment XY of length 8 cm.
2. Using a compass, place the center of the compass on point X and draw an arc with a radius of 8 cm.
3. Without changing the compass width, place the compass on point Y and draw another arc that intersects the previous one.
4. Label the point of intersection as Z.
5. To construct a point equidistant from XY and XZ, use a ruler and draw a perpendicular bisector to XY. To do this, open the compass to a width greater than half of XY and draw arcs on either side of XY.
6. Without changing the compass width, place the compass on each intersection point of the arcs and draw arcs that intersect each other. This will create two new points of intersection, one above XY and one below.
7. Label the point above XY as P.
To construct a circle touching the three sides of the triangle, follow these steps:
1. Place the center of the compass on point P and adjust the compass width to reach one of the vertices of the triangle, let's say X.
2. Draw a circle with this radius by keeping the compass width fixed.
3. Without changing the compass width, move the compass to point Y and draw another circle with the same radius.
4. Finally, move the compass to point Z and draw a third circle with the same radius.
5. The point of intersection between these three circles is the center of the circle that touches all three sides of the triangle.
6. Measure the distance from the center of the circle to any of the sides of the triangle using a ruler. This distance is the radius of the circle.
Measure the radius of the circle using a ruler to find the required measurement.