Geometry review for 1/13

for study :)

equidistant

equally distant

Verticies

The corners or points where edges meet

Circumcenter

The point where the perpendicular bisectors of a triangle intersect. It is equidistant to the vertices of a triangle

Incenter

The point where the angle bisectors of a triangle intersect. It is equidistant to the sides of the triangle.

Centroid

The point where the medians of a triangle intersect. The distance from the vertex to the centroid is twice the distance from the centroid to the midpoint.

If Centers of triangle problem is not straightforward use

The Pythagorean theorem a2 + b2 = c2

point of concurrency

the point where three lines intersect

perpendicular

Two lines intersecting to form right angles

Midpoint

The point on a segment that splits the segment into two congruent parts

perpendicular bisector

A line that is perpendicular to a segment at its midpoint.

angle bisector

a ray that splits an angle into two congruent angles

Median

a segment that connects a vertex of a triangle to the midpoint of the opposite side

Triangle inequality rule 1

The largest angle is across from the longest side of the triangle. The smallest angle is across from the shortest side of the triangle.

Triangle inequality rule 2

The sum of the two smaller sides of a triangle must be greater than the longest side.

5 ways to prove triangles congruent

SSS, SAS, ASA, AAS, HL

CPCTC

corresponding parts of congruent triangles are congruent

angle bisector

A ray that splits an angle into two congruent angles

complemantary angles

two angles that add up to 90 degrees

supplementary angles

two angles that add up to 180 degrees

Vertical Angle Theorem (VAT)

Vertical angles are congruent

Linear Pair Postulate (LPP)

If two angles form a linear pair, then they are supplementary

PCA

If lines are parallel, then Each pair of corresponding angles is congruent

PAIA

If lines are parallel, then Each pair of alternate interior angles is congruent

PAEA

If lines are parallel, then Each pair of alternate exterior angles is congruent

PCIA

If lines are parallel, then Each pair of consecutive interior angles are supplementary

Triangle Sum Theorem (TST)

The three angles of a triangle add to 180 degrees

Exterior Angle Theorem (EAT)

An exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles