Mathematics 10 Page 1 of 6 Geometric ctivities ompass can be used to construct lengths, angles and many geometric figures. (eg. Line, cirvle, angle, triangle et s you are going through the activities, record the following terms into your notebook. Perpendicular/right bisector, circumcentre Median, centroid ltitude, orthocentre ngle bisector, incentre For today s activities, you will need to know how to Find the midpoint of a line segment onstruct a perpendicular line segment Find the perpendicular bisector or right bisector Determine the concurrent oncurrent: When three or more lines meet at a single point, they are said to be concurrent. In a triangle, the three medians, three perpendicular bisectors, three angle bisectors, and three altitudes are each concurrent. Perpendicular (right) bisector: The perpendicular bisector is a line that divides a line segment into two equal parts. It also makes a right angle with the line segment. Median: median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. triangle therefore has three medians. ltitude: n altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the base. ngle isector: also called the internal angle bisector, is the line or line segment that divides the angle into two equal parts. ctivity 1: asic Practice 1. onstruct the midpoint of each of the following line segment. 1 2 Mid point (M) of a line segment
Mathematics 10 Page 2 of 6 Geometric ctivities 2. onstruct a line segment that is perpendicular to the given line segment through the given point. 2 1 Perpendicular line passes where is on the line. 4 2 1 f) Perpendicular line passes where is not on the line. e). onstruct a line segment that bisects each angle (ie. Divide each angle into two equal angles.) 2 ngle bisector from 4 1
Mathematics 10 Page of 6 Geometric ctivities 4. onstruct the perpendicular bisector of each line segment. 1 2 Mid point (M) of a line segment also creates perpendicular right bisector of. ctivity 2: ircumcentre of a Triangle ircumcentre of a triangle can be found by the intersection of the perpendicular bisectors of each side of the triangle. ircumcentre 5. Locate the circumcentre of each triangle by drawing the perpendicular bisectors of all three sides of the triangle. 6. Use the circumcentre as the centre and the distance from the circumcentre to vertex as the radius, draw a circle. This circle is called the circumcircle. What do you notice about the three perpendicular bisectors of any triangle? What is the purpose of finding circumcentre? (ie. Location, distance, angles?)
Mathematics 10 Page 4 of 6 Geometric ctivities ctivity : entroid of a Triangle The centroid of a triangle is the intersection of the three medians of the triangle. 7. For each triangle, construct the median from vertex. entroid 8. Locate the centroid of each triangle by drawing the medians from all three vertices of the triangle. 9 What do you notice about the three medians of any triangle? What do you notice about the centroid? (ie. Location, distance, angles?)
Mathematics 10 Page 5 of 6 Geometric ctivities ctivity 4: Orthocentre of a Triangle The three altitudes intersect in a single point, called the orthocenter of the triangle. 10. For each triangle, construct the altitude from vertex. Orthocenter 11. Locate the orthocentre of each triangle by drawing the altitudes from all three vertices of the triangle. 12 What do you notice about the three altitudes of any triangle? What do you notice about the orthocentre? (ie. Location, distance, angles?)
Mathematics 10 Page 6 of 6 Geometric ctivities ctivity 5: Incentre of a Triangle Incentre is the point where the three angle bisectors of a triangle meet. 1. For each triangle, construct the angle bisector of. Incentre 14. Locate the incentre of each triangle by drawing the angle bisectors from all three vertices of the triangle. 15) Use the incentre as the centre, and the distance from the incentre to vertex as the radius, draw a circle. This circle is called the incircle. What do you notice about the angle bisectors of any triangle? What do you notice about the incentre? (ie. Location, distance, angles?)