Construct a triangleABC, AB=6 cm, angleA=60 degree, angleB=70 degree. And also find the centroid, orthocentre, curcumcentre and perpendicular of the triangle.
Assuming you can do basic constructions like bisecting a line or construct a perpendicular at a point, the following page should get you on your way.
http://jwilson.coe.uga.edu/EMAT6680/Dunbar/Assignment4/Assignment4_KD.htm
google is your friend -- use it.
To construct Triangle ABC, follow these steps:
1. Draw a line segment AB of length 6 cm.
2. At point A, use a protractor to measure an angle of 60 degrees and mark a point as C on one side of the angle.
3. At point B, use a protractor to measure an angle of 70 degrees and mark a point as C on one side of the angle.
4. Draw lines from point C to points A and B to complete the triangle ABC.
Now, let's find the properties of Triangle ABC:
Centroid:
The centroid of a triangle is the point of intersection of its medians. A median is a line drawn from a vertex to the midpoint of the opposite side. To find the centroid:
1. Locate the midpoint of each side of the triangle (label them as D, E, and F).
2. Draw lines from each vertex (A, B, and C) to their respective midpoints (D, E, and F).
3. The point of intersection of these three lines is the centroid (label it as G).
Orthocenter:
The orthocenter of a triangle is the point of intersection of its altitudes. An altitude is a perpendicular line drawn from a vertex to the opposite side. To find the orthocenter:
1. Draw a perpendicular line (altitude) from each vertex (A, B, and C) to its opposite side.
2. The point of intersection of these three altitudes is the orthocenter (label it as H).
Circumcenter:
The circumcenter of a triangle is the point of intersection of the perpendicular bisectors of its sides. To find the circumcenter:
1. Bisect each side of the triangle (label the points of division as P, Q, and R).
2. Draw perpendicular lines to each side at points P, Q, and R.
3. The point of intersection of these three perpendicular bisectors is the circumcenter (label it as O).
Perpendicular Bisectors:
A perpendicular bisector is a line that passes through the midpoint of a segment and is perpendicular to that segment. To locate the perpendicular bisectors:
1. Locate the midpoint of each side of the triangle (label them as D, E, and F).
2. Draw a line perpendicular to each side, passing through its corresponding midpoint.
Now you have constructed Triangle ABC and found its centroid, orthocenter, circumcenter, and perpendicular bisectors.