IM Geo.6.17 Lesson: Lines in Triangles
If you have tracing paper, draw a triangle on it. Fold the altitude from each vertex. If not, observe the applet below.
Triangle ABC is graphed.
Find the slope of each side of the triangle.
Find the slope of each altitude of the triangle.
Write equations for all 3 altitudes.
Use the equations to find the coordinates of and verify algebraically that the altitudes all intersect at .
Any triangle can be translated, rotated, and dilated so that the image lies on the origin, lies on the point , and has position . Use this as a starting point to prove that the altitudes of all triangles all meet at the same point.
Triangle ABC is graphed.
Find the midpoint of each side of the triangle.
Write equations for all 3 perpendicular bisectors.
Use the equations to find the coordinates of and verify algebraically that the perpendicular bisectors all intersect at .
Consider triangle ABC from an earlier activity.
What is the distance from to , the intersection point of the perpendicular bisectors of the triangle’s sides? Round to the nearest tenth.
Write the equation of a circle with center and radius .
What do you notice?
Verify your hypothesis algebraically.
Consider triangle ABC from earlier activities.
What seems to be true about points , , and ?
Prove that your observation is true.
A tessellation covers the entire plane with shapes that do not overlap or leave gaps.
Write the equations for lines that outline 1 rectangle.
Write the equations for lines that outline 1 right triangle.
Write the equations for lines that outline 1 of the shapes.