Special Segments in Triangles
Lesson Plan
Directions for activity:
1. The students will cut out the four triangles provided for them. These triangles are scalene (meaning they have no two sides congruent to each other).
2. First, the students need to fold a triangle to create the altitudes. Start by explaining the definition of an altitude and then ask the students to describe how they think an altitude can be created from each vertex. By its definition, an altitude is created by folding the triangle to create a segment from a vertex of the triangle to the opposite side so that the segment is perpendicular to that side (or forms a 90 degree angle with the side). This process can be accomplished by using the corner of a piece of paper (which is a 90 degree angle). This needs to be done three different times since there are three different vertices; therefore, yielding three altitudes. The point at which the three altitudes intersect is called the orthocenter. This should be written on the back of the folded triangle.
3. Next, the students need to create the medians of a triangle. Start by explaining the definition of a median and then ask the students to describe how they think a median can be created from each vertex. By its definition, a median segment starts at a vertex and goes to the midpoint of the opposite side of the triangle. The students can fold the triangle so that they first find the midpoint of each side. Then they need to fold the triangle so that a segment is created from the vertex to that midpoint. Three medians should be created, one from each vertex. The medians intersect at a point called the centroid. This should be written on the back of the folded triangle.
4. There is a special relationship that occurs with the median. Each student should measure the distance from the vertex to the centroid and then the distance from the centroid to the side. There is a relationship (ratio) that can be found between these measurements that is true for all medians. The ratio that should be found is 2/3.
5. Last, the students will need to create the angle bisectors of the triangle. Again there will be three formed in each triangle. By its definition, an angle bisector cuts an angle into two congruent angles. Therefore, the students need to create a segment by folding the third triangle so that a segment is created from each vertex so that each angle is congruent. The point at which the three angle bisectors intersect is called the incenter. This should be written on the back of the folded triangle.
Now the students have created each set of segments for the triangles. They have the intersection point labeled and can use these triangles as a study guide for their test.
SHEET OF TRIANGLES