Using a ruler and a pair of compass only construct a triangle PQR with |PQ|=5•5cm, |PR|=6•5cm and angle QPR=120°•A point S on QR such that it is equidistant from|PQ| and |PR|
Useless page better put pictures Nonsense!!!???😠😠😠😠😠😠
draw PQ
with center at P, draw a circle of radius |PR|. R will lie somewhere on that circle.
Now construct a 120° angle at Q. Where its ray meets the circle will be R.
Now just bisect QR to find point S.
I assume you can construct a 60° angle, so doubling it will be easy.
There are many examples online of constructing a perpendicular bisector.
To construct a triangle PQR with |PQ|=5•5cm, |PR|=6•5cm, and angle QPR=120°, along with a point S on QR that is equidistant from |PQ| and |PR|, follow these steps:
1. Take a ruler and draw a line segment PQ of length 5•5cm.
2. Place the compass at point P and open it to a length of 6•5cm. Draw an arc intersecting PQ.
3. Without changing the compass width, place the compass at the intersecting point and draw another arc intersecting the previous arc. Label this point of intersection as R.
4. Join points P and R with a straight line to form segment PR.
5. To construct the equidistant point S on QR, place the compass tips at point P and adjust it to a width greater than half of PR.
6. Draw arcs on either side of PR, intersecting QR. Label these points of intersection as S1 and S2.
7. Use the compass to measure the distance from point S1 to both PQ and PR.
8. Keeping the compass at the same width, place the compass at point S2 and draw arcs intersecting PQ and PR.
9. The intersection point on PQ is the desired point S. Mark it as S.
10. Finally, join points P and S with a straight line.
You have now successfully constructed triangle PQR with |PQ|=5•5cm, |PR|=6•5cm, angle QPR=120°, and a point S on QR that is equidistant from |PQ| and |PR|.
To construct triangle PQR with the given measurements and point S, you will need a ruler and a compass. Follow these steps:
1. Start by drawing a line segment PQ of length 5•5cm using the ruler. Mark point P at one end and point Q at the other.
2. With point P as the center, draw an arc with radius 6•5cm using the compass. This arc should intersect line segment PQ.
3. Without changing the compass width, place the compass point on the intersection of the arc and PQ, and draw another arc intersecting the previous arc. Label this intersection point as R.
4. Now, using the compass, adjust the width to a distance greater than half of the length of line segment PQ (5•5cm in this case). Place the compass point on point P and draw an arc, cutting line segment PQ on both sides.
5. Repeat the previous step, but this time with point R as the center. Draw an arc cutting line segment PQ on both sides.
6. The intersection point of the two arcs on line segment PQ will be the point S, which is equidistant from points P and R.
7. Connect point S with points P and R to complete the triangle PQR.
Congratulations! You have successfully constructed triangle PQR with the measurements given and point S equidistant from segments PQ and PR using only a ruler and compass.