Points of Concurrency

DON'T FORGET:

* The congruency marks on the sides of a triangle are all going to be different since all of the side lengths are different (unless it's an equilateral triangle) * Also, the angle congruency marks will be different

To prove two circles similar:

- The reduced ratio of the diameters and circumferences (C=2πr)are *proportional* - All *corresponding* angles are congruent

Orthocenter

Created by: Point of concurrency of the *altitudes* of a triangle Additional Information: - If the triangle is *acute*, the orthocenter is *inside* the triangle - If the triangle is *right*, the orthocenter is *on* the triangle - If the triangle is *obtuse*, the orthocenter is *outside* the triangle

Centroid

Created by: Point of concurrency of the medians of a triangle Characteristics: Divides the medians into a 2:1 ratio from each vertex Additional Information: - The centroid always falls *inside* the triangle - The centroid is considered to be a triangle's "center of gravity" (balancing point)

Circumcenter

Created by: Perpendicular bisectors of the sides of a triangle Characteristics: - The circumcenter is the center of a circle circumscribed about a triangle - *Equidistant* to the *vertices* of a triangle Additional Information: - If the triangle is *acute*, the circumcenter is *inside* the triangle - If the triangle is *right*, the circumcenter is *on* the triangle - If the triangle is *obtuse*, the circumcenter is *outside* the triangle

Incenter

Created by: The angle bisectors of a triangle Characteristics: - The incenter is the center of a circle that is inscribed in a triangle - *Equidistant* to the *sides* of a triangle Additional Information: - The incenter always falls *inside* of a triangle

Median

Each median represents the *segment* joining the *midpoint of a side* to the *opposite vertex*

Altitude

Line that *passes through a vertex* of a triangle and is *perpendicular to the opposite side*

Circumscribed

Within, around

As the number of _______ of an inscribed polygon increases, its ______ increases until it begins to approximate the area of the circle inside which it is inscribed.

sides, area

the more the ________, the less the _________________ of shaded area

sides, percentage