warm up problems 22- 28 in eoc packet. essential questions: what are the different types of triangle...

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Problems 22- 28 in EOC packet

Essential Questions: Essential Questions: What are the different types of

triangle centers and how do I construct them?

Standard(s): 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 Unit 1 Section 7 Triangle Centers

VocabularyVocabulary 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.

CircumcenterCircumcenterWhat is a circumcenter?Hint: What is it the center of?

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CircumcenterCircumcenterWhere is the circumcenter

located ona) An acute triangleb) An obtuse trianglec) A right triangle

Inside the triangle

Outside the triangle

On the triangle

CentroidCentroidWhat is special about the

medians that make a centroid?Hint: There is a ratio involved

IncenterIncenterFormed by:Angle Bisectors

What is special about the incentor?

It is the center of a triangle that tangents all the sides

Properties of the IncenterProperties of the IncenterThe 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

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OrthocenterOrthocenterWhat forms an orthocenter?Altitudes

Shortcut:Instead of drawing all three altitudes two will also show the accurate orthocenter

OrthocenterOrthocenterThe 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

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