Bell work: Find the missing length

5-4: Medians and Altitudes

The median of a triangle is a cross between the angle and perpendicular bisectors; a line segment whose endpoints are a vertex and midpoint of the opposite side The 3 medians of a triangle intersect at a point called the centroid, which is always inside the triangle An altitude of a triangle is the perpendicular segment from a vertex to the line containing the opposite side. They can be inside, outside, or on the side of a triangle.

Finding the length of a median XA =10 What is XB? If CZ=30, what is ZA? CA?

Altitude vs Median What is AD? EG? CF?

The point where the altitudes of the triangle are concurrent is called the orthocenter. The orthocenter can be inside, on, or outside the triangle.

5-3: Bisectors in Triangles

How many perpendicular bisectors does a triangle have? 3, one going through each side Do they all intersect, or only certain combinations? All 3 intersect at a point called the circumcenter

When three or more lines intersect, they are said to be concurrent When three or more lines intersect, they are said to be concurrent. The location they intersect at is the point of concurrency The point where the three perpendicular bisectors intersect is the circumcenter of the triangle Circumscribed about a shape means drawing another shape around the endpoints

Circumcenters can be anywhere!

How to find the circumcenter What are the coordinates of the circumcenter of the triangle with vertices P(0,6), O(0,0), and S(4,0)? What are the coordinates of the circumcenter of the triangle with vertices A(2,7), B(10,7), and C(10,3)?

A circle circumscribed within a triangle has its center at the circumcenter

How many ANGLE bisectors does a triangle have? 3, one going through each angle Do they all intersect, or only certain combinations? All 3 intersect at a point called the incenter

The incenter of the triangle is the point where all three angle bisectors are concurrent(where they intersect) The incenter will always be inside the triangle Inscribed in a shape means drawing another shape inside the first

Ge=2x-7 GF=x+4 What is GD? What is the incenter of the triangle? Is the circumcenter located on this diagram? If so, what is it?

Summary Homework: Triangle Segments Worksheet