Geometry Unit 6 Review

Incenter

created by angle bisectors; needs right angles and congruent angles; equidistant from a triangle’s sides; always inside; center of an inscribed circle

Circumcenter

created by perpendicular bisectors; needs midpoints and right angles; equidistant from a triangle’s vertices; acute: inside, obtuse: outside, right: midpoint of hypotenuse

Centroid

Created by medians; needs midpoints; always inside; center of gravity/balance; vertex to centroid = 2/3 of the median

Orthocenter

Created by altitudes; needs right angles; vertex connected to the opposite side so it is perpendicular; acute: inside, obtuse: outside, right:on the right angle

To say segments are parallel, you need to prove

Equal slopes

To say one segment is half the length of another segment, you need to prove

Distance formula

You use the Hinge Theorem when given

Angles

You use the Converse Hinge Theorem when given

Sides

Centroid formula

(X₁+X₂+X₃)/3 , (Y₁+Y₂+Y₃)/3