Lesson 27/28 Special Segments in Triangles

Transcription

1 Lesson 27/28 Special Segments in Triangles ***This is different than on your notetaking guide***

2 PART 1 - VOCABULARY

3 Perpendicular Angle Median Altitude Circumcenter Incenter Centroid Orthocenter

4 A line that is perpendicular to a segment at its midpoint. Angle Median Altitude Circumcenter Incenter Centroid Orthocenter

5 A ray that divides an angle into two congruent angles Perpendicular Median Altitude Circumcenter Incenter Centroid Orthocenter

6 A segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side. Perpendicular Angle Altitude Circumcenter Incenter Centroid Orthocenter

7 Acute Triangle All of the altitude are inside the triangle A perpendicular segment from a vertex of a triangle to the line containing the opposite side. Perpendicular Angle Median Right Triangle two of the altitudes are legs of the triangle. Circumcenter Incenter Centroid Orthocenter Obtuse Triangle two of the altitudes are outside the triangle.

8 Is AB as a median, altitude, angle bisector, or perpendicular bisector?

9 Concurrent the point at which three or more lines intersect. For any triangle, certain sets of lines are always concurrent.

10 A line that is perpendicular to a segment at its midpoint. Angle Median Altitude Incenter Centroid Orthocenter The point of concurrency of the perpendicular bisectors.

11 A ray that divides an angle into two congruent angles Perpendicular Median Altitude Circumcenter Centroid Orthocenter The point of concurrency of the angle bisectors.

12 A segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side. Perpendicular Angle Altitude Circumcenter Incenter Orthocenter The point of concurrency of the medians.

13 A perpendicular segment from a vertex of a triangle to the line containing the opposite side. Perpendicular Angle Median Circumcenter Incenter Centroid The point of concurrency of the altitudes.

14 All of My children Are Bringing In Peanut Butter Cookies = = = = "All of my children are bringing in peanut butter cookies." Altitudes, Orthocenter Medians, Centroid Angle s, Incenter Perpendicular s, Circumcenter ***Be careful not to mix up centroid and circumcenter*** More Acronyms

15 Explore Are the points of concurrency always inside the triangle?

16 Perpendicular Angle Median Altitude Circumcenter Incenter Centroid Orthocenter can be outside always inside always inside can be outside of the triangle the triangle the triangle of the triangle

17 PRACTICE

18 perpendicular bisector angle bisector none PR QT altitude median

19 angle bisector H AD EG CF HD median none altitude perpendicular bisector

20 Classify each red segment as a median, altitude, angle bisector, perpendicular bisector, or neither. angle bisector none altitude perpendicular bisector median

21 The point of concurrency of the perpendicular bisectors is the. circumcenter The point of concurrency of the altitudes is the. orthocenter The point of concurrency of the medians is the. centroid The point of concurrency of the angle bisectors is the. incenter

22 Which point is the centroid?

23 Which point is the orthocenter?

24 Homework: *Lesson 26 PRACTICE *Lesson 27/28 PRACTICE 1 *Study the 8 vocabulary words on the foldable You may want to use an acronym to help!

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