1. Lines, Angles and Triangles
Special Segments in Triangles
Opening routine

2. Topic III: Lines, Angles and Triangles

3. Lines, Angles and Triangles
Special Segments in Triangles
Objectives: Identify and use perpendicular bisectors, angle bisectors, medians and altitudes in triangles.
Essential Question: How can I use points of
concurrency in triangles?

4. Lines, Angles and Triangles
Special Segments in Triangles
Perpendicular Bisectors and Angle Bisectors
Vocabulary
Perpendicular bisector: Is a segment that passes by the midpoint of a side and is perpendicular to that side. They are concurrent.
Circumcenter: Is the point of concurrency of the perpendicular bisectors of a triangle. It is equidistant from the vertices of the triangle.

5. Lines, Angles and Triangles
Special Segments in Triangles
Vocabulary
Angle bisector: Is a bisector to any of the angles of the triangle. Any point on the angle bisector is equidistant from the sides of the angle. They are concurrent.
Incenter: Is the point of concurrency of the angle bisectors. It is equidistant from the sides of the triangle.

6. Lines, Angles and Triangles
Special Segments in Triangles
Vocabulary
Median: Is a segment whose endpoints are a vertex of a triangle and the midpoint of the side opposite the vertex. They are concurrent.
Centroid: Is the point of concurrency of the medians of a triangle. It is the point of balance of any triangle.

7. Lines, Angles and Triangles
Special Segments in Triangles
Vocabulary
Altitude: Is a segment that joins a vertex of a triangle with the opposite side and is perpendicular to that side.
Orthocenter: Is the point of concurrency of the altitudes of a triangle.
Midsegment: Is a segment that joins the midpoints of two sides of the triangle. Every triangle has three midsegments, which form the midsegment triangle.

8. Lines, Angles and Triangles
Special Segments in Triangles
Perpendicular Bisectors and Angle Bisectors

9. Lines, Angles and Triangles
Special Segments in Triangles
Perpendicular Bisectors and Angle Bisectors

10. Lines, Angles and Triangles
Special Segments in Triangles
Perpendicular Bisectors and Angle Bisectors

11. Lines, Angles and Triangles
Special Segments in Triangles
Perpendicular Bisectors and Angle Bisectors

12. Lines, Angles and Triangles
Special Segments in Triangles
Perpendicular Bisectors and Angle Bisectors

13. Lines, Angles and Triangles
Special Segments in Triangles
Medians, Altitude and Midsegments

14. Lines, Angles and Triangles
Special Segments in Triangles
Medians, Altitude and Midsegments

15. Lines, Angles and Triangles
Special Segments in Triangles
Medians, Altitude and Midsegments

16. Lines, Angles and Triangles
Special Segments in Triangles
Medians, Altitude and Midsegments

17. Lines, Angles and Triangles
Special Segments in Triangles
Medians, Altitude and Midsegments

18. Lines, Angles and Triangles
Special Segments in Triangles
Medians, Altitude and Midsegments
Guided Practice – WE DO
What is the orthocenter of
the triangle with two altitudes
given by the lines x = 1 and
y = x + 1?
(1, 2)
(1, 0)
(0, 1)
None of these

19. Lines, Angles and Triangles
Special Segments in Triangles
Independent Practice - YOU DO
Worksheet “Review Topic III”
Exercises from 1 to 20

20. Quadrilaterals and Coordinates Proof
Coordinates Proof for Parallelograms
Closure
Essential Question: What criteria can be used in a coordinate proof to determine of a quadrilateral is a parallelogram?