1. Warm up: Solve for x.
Linear Pair
4x + 3
7x + 12
X = 15

2. Special Segments in Triangles

3. Median
Connect vertex to
opposite side's
midpoint

4. Altitude
Connect vertex to
opposite side and is
perpendicular

5. The altitude is the “true height” of the triangle.
Tell whether each red segment is an altitude of the triangle.
The altitude is the “true height” of the triangle.
YES NO
YES

6. Perpendicular Bisector
Goes through the
midpoint and is
perpendicular

7. Tell whether each red segment is an perpendicular bisector of the triangle.NO NO
YES

8. Angle Bisector
Cuts the angle
In to TWO
congruent parts

9. Start to memorize…
Indicate the special triangle segment based on its description

10. I cut an angle into two equal parts
Who am I?
I cut an angle into two equal parts
Angle Bisector

11. I connect the vertex to the opposite side’s midpoint
Who am I?
I connect the vertex to the opposite side’s midpoint
Median

12. I connect the vertex to the opposite side and I’m perpendicular
Who am I?
I connect the vertex to the opposite side and I’m perpendicular
Altitude

13. Perpendicular Bisector
Who am I?
I go through a side’s midpoint and I am perpendicular
Perpendicular Bisector

14. Drill & Practice
Indicate which special triangle segment the red line is based on the picture and markings

15. Multiple Choice Identify the red segment
Q1:
Angle Bisector B. Altitude
C. Median D. Perpendicular Bisector

16. Multiple Choice Identify the red segment
Q2:
Angle Bisector B. Altitude
C. Median D. Perpendicular Bisector

17. Multiple Choice Identify the red segment
Q3:
Angle Bisector B. Altitude
C. Median D. Perpendicular Bisector

18. Multiple Choice Identify the red segment
Q4:
Angle Bisector B. Altitude
C. Median D. Perpendicular Bisector

19. Multiple Choice Identify the red segment
Q5:
Angle Bisector B. Altitude
C. Median D. Perpendicular Bisector

20. Multiple Choice Identify the red segment
Q6:
Angle Bisector B. Altitude
C. Median D. Perpendicular Bisector

21. Multiple Choice Identify the red segment
Q7:
Angle Bisector B. Altitude
C. Median D. Perpendicular Bisector

22. Multiple Choice Identify the red segment
Q8:
Angle Bisector B. Altitude
C. Median D. Perpendicular Bisector

23. Points of Concurrency

24. New Vocabulary (Points of Intersection)
Centroid
Orthocenter
Incenter
Circumcenter

25. Point of Intersection
Medians
intersect at the
centroid

26. Important Info about the Centroid
The intersection of the medians.
Found when you draw a segment from one vertex of the triangle to the midpoint of the opposite side.
The center is two-thirds of the distance from each vertex to the midpoint of the opposite side.
Centroid always lies inside the triangle.
This is the point of balance for the triangle.

27. The intersection of the medians is called the CENTROID.

28. Altitudes orthocenter
Point of Intersection
Altitudes
intersect at the
orthocenter

29. Important Info about the Orthocenter
This is the intersection point of the altitudes.
You find this by drawing the altitudes which is created by a vertex connected to the opposite side so that it is perpendicular to that side.
Orthocenter can lie inside (acute), on (right), or outside (obtuse) of a triangle.

30. The intersection of the altitudes is called the ORTHOCENTER.

31. Angle Bisector incenter
Point of Intersection
Angle Bisector
intersect at the
incenter

32. Important Info about the Incenter
The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle.
Incenter is equidistant from the sides of the triangle.
The center of the triangle’s inscribed circle.
Incenter always lies inside the triangle

33. The intersection of the angle bisectors is called the INCENTER.

34. Perpendicular Bisectors
Point of Intersection
Perpendicular Bisectors
intersect at the
circumcenter

35. Important Information about the Circumcenter
The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle.
The circumcenter is the center of a circle that surrounds the triangle touching each vertex.
Can lie inside an acute triangle, on a right triangle, or outside an obtuse triangle.

36. The intersection of the perpendicular bisector is called the CIRCUMCENTER.

37. Memorize these! MC AO ABI PBCC Medians/Centroid Altitudes/Orthocenter
Angle Bisectors/Incenter
Perpendicular Bisectors/Circumcenter

38. Will this work? MC AO ABI PBCC My Cousin Ate Our Avocados But I
Prefer Burritos Covered in Cheese