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Section 1.5 Special Points in Triangles

Section 1.5 Special Points in Triangles. CONCURRENT. The point where 3 or more lines intersect. TRIANGLES & CIRCLES. What are some things you already know about triangles or circles?. PREVIOUS FACTS…. How many sides does a triangle have? What kinds of triangles are there?.

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Section 1.5 Special Points in Triangles

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  1. Section 1.5Special Points in Triangles

  2. CONCURRENT • The point where 3 or more lines intersect

  3. TRIANGLES & CIRCLES What are some things you already know about triangles or circles?

  4. PREVIOUS FACTS… • How many sides does a triangle have? • What kinds of triangles are there?

  5. WHAT IS A PERPENDICULAR BISECTOR??

  6. PERPENDICULAR BISECTOR • Forms right angles. • Splits the segment in half

  7. PERPENDICULAR BISECTORS & TRIANGLES Now let’s combine perpendicular bisectors and triangles.

  8. BEGIN BY… • Finding the perpendicular bisector of each side of the triangle.

  9. WHAT CAN WE CONCLUDE? • What happens when these 3 lines intersect? What is formed?

  10. Perpendicular Bisectors • The perpendicular bisectors of a triangle ____________ at a single __________.

  11. EXAMPLE

  12. CIRCUMCENTER • The intersection point of the perpendicular bisectors of a triangle

  13. Circumcenter of an Obtuse Triangle

  14. WHAT IS A ANGLE BISECTOR??

  15. ANGLE BISECTOR • Splits the angle in half

  16. ANGLE BISECTORS & TRIANGLES Now let’s combine angle bisectors and triangles.

  17. BEGIN BY… • Finding the angle bisector of each angle of the triangle.

  18. WHAT CAN WE CONCLUDE? • What happens when these 3 lines intersect? What is formed?

  19. The angle bisectors of a triangle __________ at a single _________. Angle Bisector

  20. EXAMPLE

  21. INCENTER • The intersection point of the angle bisectors of a triangle

  22. INSCRIBED & CIRCUMSCRIBED CIRCLES

  23. INSCRIBED • Inside the triangle • Just touches the three sides of the triangle.

  24. INCENTER • Another definition of Incenter: • The center of an inscribed circle

  25. CIRCUMSCRIBED • Outside the triangle • Contains all 3 vertices

  26. CIRCUMCENTER • The center of a circumscribed circle

  27. A couple of other definitionsyou need to know

  28. Altitude • A perpendicular line segment from a vertex of a triangle to the line containing the opposite side. • How many altitudes can a triangle have?

  29. Median • A line segment from a vertex to the midpoint of the opposite side.

  30. Centroid • The point where the 3 medians meet

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