geometry Module 5

ANGLES AND SIDES:

• the sum of the measures of the interior angles of a triangle is 180.

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

• Two figures are conveyed if and only if there is a rigid transformation or series of rigid transformations that maps one figure exactly onto the other.

• In two congruent polygons. All the parts of one polygon are congruent to the corresponding parts of the other polygon.

WAYS TO PROVE TRIANGLES CONGRUENT:

• (SSS) - three sides of one triangle congruent to three sides of a second triangle.

• (SAS) - two sides and the included angle of one triangle congruent to two sides and the included angle of a second triangle.

• (ASA) - two angles and the included side of one triangle congruent to two angles and the included side of a second triangle.

• (AAS) - two angles and the non included side of one triangle congruent to two angles and the non included side of a second triangle.

RIGHT TRIANGLES:

• Leg-Leg Congruence (LL)

• Hypotenuse-Angle Congruence (HA)

• Leg-Angle Congruence (LA)

• Hypotenuse-Leg Congruence (HL)

ISOSCELES AND EQUILATERAL TRIANGLES:

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

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

• Each angle of an equilateral triangle measures 60 degrees.

COORDINATE PROOF:

• To write a coordinate proof: Place the figure on the coordinate plane. Label the vertices. Use algebra to prove properties of theorems.