3.2 - 3.4 Quiz Review

Review Flashcards Covering Notes 3.2-3.4. Before starting, make sure to click shuffle to mix up the order of the cards.

Median

a segment that connects a vertex to the opposite side’s midpoint

Triangles have ______ medians

3

Centriod

“Ce” - the intersection of 3 medians

Fun Facts of the Ce:

1. The centroid is the perfect _________

2. The distance from ____________ is _________ the distance from ____________ (__:__)

3. All __ ________ created by the Ce have __________

4. The Ce is always located _______________

5. The sum of ___________ is always greater than the ________ of the triangle

1. the centroid is the perfect center of mass

2. the distance from the vertex to the centroid is twice the distance from the centroid to the midpoint (2:1)

3. all 6 triangles created by the Ce have the same area

4. the Ce is always located in the interior of the triangle

5. the sum of the medians is always greater than the perimeter of the triangle

Ce Formula

Angle Bisector

a segment that bisects an angle of a triangle

Incenter

“Ic” - the intersection of the 3 angle bisectors

A triangle has ______ angle bisectors

3

Fun Facts of the Ic

1. the incenter is always in the interior of the triangle

2. the incenter is the center of a circle that fits perfectly in the triangle

3. the incenter is equidistant to all 3 triangle sides (radii)

Altitude

a segment that connects a vertex to the opposite side (or the extension of the opposite side) at a right angle

Orthocenter

“Oc” - the intersection of 3 altitudes

Location of the Oc

Acute - inside

Obtuse - outside

Right - on the rt. angle

Perpendicular Bisectors

a line that bisects one side of a triangle at a right angle

A perpendicular bisector does not have to….

….originate from a vertex of the triangle

Circumcenter

“Cc” - the intersection of the 3 perpendicular bisectors

Fun Facts of the Cc

1. the circumcenter is the center of a circle outside of the triangle

2. the circumcenter is equidistant to the 3 triangle verticies

Location of the Cc

Acute - inside

Obtuse - outside

Right - midpoint of the hypotenuse

If I draw in all the medians, all the angle bisectors, all the altitudes, and all the perpendicular bisectors in a [scalene, isoceles, equilateral] triangle, then I will draw ____ segments

Scalene: 12 segments

Isoceles: 9 segments

Equilateral: 3 segments

Name the (a) 4 segment names, (b) the applicable point, and (c), the point abbreviation

Define: SSS, SAS, ASA, AAS

SSS: Side, Side, Side

SAS: Side, Included Angle, Side

ASA: Angle, Included Side, Angle

AAS: Angle, Angle, Non-Included Side

C.P.C.T.C. (Define)

Corresponding Parts of Congruent Triangles are Congruent

Radii Theorem

All radii of a circle are ≅

Area and Circumference Formulas

A = πr²

C = πd (or 2πr)

Line Postulate

2 pts determine a line

The centroid is always located….

inside the triangle

The incenter is always….

inside the triangle

In a proof, writing def of [median, angle bisector, altitude, perpendicular bisector] results in

Median: 2 segments congruent

Angle Bisector: 2 angles congruent

Altitude: 2 angles right

Perp. Bisector: 2 segments congruent, 2 angles right

Which three points are always collinear? What is the name of the line that they form?

a: Oc, Ce, Cc

b: Euler’s Line

The Ic is only on Euler’s Line if…

…the triangle is isoceles

In Euler’s Line, the distance from the __ to the __ is twice the distance from the __ to the __

In Euler’s Line, the distance from the Oc to the Ce is twice the distance from the Ce to the Cc

The center of a ____-_____ ______ lies on the ________ of Euler’s segment

The center of a nine-point circle lies on the midpoint of Euler’s segment

In what triangle is there no Euler’s Line?

Equilateral