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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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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?
PERPENDICULAR BISECTOR • Forms right angles. • Splits the segment in half
PERPENDICULAR BISECTORS & TRIANGLES Now let’s combine perpendicular bisectors and triangles.
BEGIN BY… • Finding the perpendicular bisector of each side of the triangle.
WHAT CAN WE CONCLUDE? • What happens when these 3 lines intersect? What is formed?
Perpendicular Bisectors • The perpendicular bisectors of a triangle ____________ at a single __________.
CIRCUMCENTER • The intersection point of the perpendicular bisectors of a triangle
ANGLE BISECTOR • Splits the angle in half
ANGLE BISECTORS & TRIANGLES Now let’s combine angle bisectors and triangles.
BEGIN BY… • Finding the angle bisector of each angle of the triangle.
WHAT CAN WE CONCLUDE? • What happens when these 3 lines intersect? What is formed?
The angle bisectors of a triangle __________ at a single _________. Angle Bisector
INCENTER • The intersection point of the angle bisectors of a triangle
INSCRIBED • Inside the triangle • Just touches the three sides of the triangle.
INCENTER • Another definition of Incenter: • The center of an inscribed circle
CIRCUMSCRIBED • Outside the triangle • Contains all 3 vertices
CIRCUMCENTER • The center of a circumscribed circle
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?
Median • A line segment from a vertex to the midpoint of the opposite side.
Centroid • The point where the 3 medians meet