UNIT 4 HONORS GEOMETRYYY

How do you write a classified triangle?

Angle first, then side. (EX: Obtuse Scalene Triangle)

exterior angle theorem

The measure of an exterior angle of a triangle is equal to the sum of the two remote interior angles.

Third angle theorem

if two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent

definition of congruent polygons

2 polygons are congruent if and only if their corresponding parts are congruent.

Triangle sum corollaries

1. The acute angles of a right triangle are complementary.

2. There can be at most one right or obtuse angle in a triangle.

Triangle sum corollaries

Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

converse of Isosceles triangle theorem

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Equilateral Triangle Corollaries

-A triangle is equilateral if and only if it is equiangular

-Each angle of an equilateral triangle measures 60

Equilateral Triangle Corollaries

Median equation

m=([x1+x2]/2, [y2+y1]/2)

Slope equation

m=y1-y2/x1-x2

distance formula

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

Which one is undefined? Vertical or Horizontal?

Vertical

Which one has the value of slope=0? Vertical or Horizontal?

Horizontal

uniquely determined

exactly one thing satisfies the given condition

Underdetermined

not placed enough conditions on an auxiliary figure.

overdetermined

there are too many conditions

What is an example of uniquely determined?

Draw a line m through E parallel to AC(segment)

What is an example of underdetermined?

Draw line l through B

What is an example of overdetermined?

Draw DB(line) parallel to AC(segment)

What is the total angle of a hexagon?

720

Do you use a transitive or a substitution in the tables?

Substitution