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Section 1.5 Special Points in Triangles. CONCURRENT The point where 3 or more lines intersect.

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Presentation on theme: "Section 1.5 Special Points in Triangles. CONCURRENT The point where 3 or more lines intersect."— Presentation transcript:

1 Section 1.5 Special 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 How many sides does a triangle have? What kinds of triangles are there? PREVIOUS FACTS…

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 Splits the angle in half ANGLE BISECTOR

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

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 Another definition of Incenter: The center of an inscribed circle INCENTER

25 CIRCUMSCRIBED Outside the triangle Contains all 3 vertices

26 The center of a circumscribed circle CIRCUMCENTER

27 A couple of other definitions you 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

31


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