Warm UP Problems in EOC packet

Essential Questions: What are the different types of triangle centers and how do I construct them?

Standard(s): MCC9-12.G.CO.12Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

Unit 1 Section 7 Triangle Centers

Vocabulary Circumcenter: Is the center of a circle that perfectly passes through each vertex. Incenter: Is the center of largest possible circle that still completely fits inside the circle. Centroid: Is the center that is the center of gravity of the triangle (balancing point) and there is a constant ratio between the distance from the centroid to the midpoint and centroid to the vertex. Orthocenter: Is the fourth common center but has no unique properties other than it is on the EULER line. MEDIAN of a triangle: All triangle’s have 3 medians. Each median is a segment with one endpoint on the midpoint of a side of a triangle and the other endpoint at the opposite vertex of the triangle ALTITUDE of a triangle: All triangle’s have 3 altitudes. Each altitude is a line that passes through a vertex of the triangle and is perpendicular to the opposite side.

Circumcenter What is a circumcenter? Hint: What is it the center of? CLICK HERE

Circumcenter Where is the circumcenter located on a)An acute triangle b)An obtuse triangle c)A right triangle Inside the triangle Outside the triangle On the triangle

Centroid What is special about the medians that make a centroid? Hint: There is a ratio involved

Incenter Formed by: Angle Bisectors What is special about the incentor? It is the center of a triangle that tangents all the sides

Properties of the Incenter The incenter is the center of the triangle's incircle, the largest circle that will fit inside the triangle and touch all three sides. Always inside the triangle CLICK HERE

Orthocenter What forms an orthocenter? Altitudes Shortcut: Instead of drawing all three altitudes two will also show the accurate orthocenter

Orthocenter The orthocenter is not always inside the triangle. If the triangle is obtuse, it will be outside. If the triangle is right it will be on the vertex of the right angle CLICK HERE