Geometry Theorems and Vocab

CPCTC

Corresponding parts of congruent triangles are congruent

Transitive Property

If Triangle ABC is congruent to Triangle EFG, and Triangle EFG is congruent to Triangle JKL, then Triangle ABC is congruent to Triangle JKL

Symmetric Property

If Triangle ABC is congruent to Triangle EFG, then Triangle EFG is congruent to Triangle ABC

Alternate Interior Angles Theorem

If a transversal intersects two parallel lines, then alternate interior angles are congruent.

Leg Angle Congruence

If one leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent

Hypotenuse Leg Congruence

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and the corresponding leg of another right triangle, then the triangles are congruent

Hypotenuse Angle Congruence

If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and the corresponding acute angle of another right triangle, then the triangles are congruent

Leg Leg Congruence

If the legs of one right angle are congruent to the corresponding legs of another right triangle, then the triangles are congruent

Side Side Side Congruence

If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent.

Angle Side Angle Congruence

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent

Angle Angle Side Congruence

If two angles and the non included side of one triangle are congruent to the corresponding two angles and non included side of a second triangle, then the two triangles are congruent.

Vertical Angles Theorem

If two angles are vertical, then they are congruent. Meaning they serve as an angle to both triangles.

Third Angles 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.

Side Angle Side Congruence

If two sides and the congruent angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.

isoscles triangle theorem

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

Corollary 5.1

The acute angles of a right triangle are complementary; they equal 90 degrees

Exterior Angles Theorom

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

Triangle Angle Sum Theorem

The sum of the measures of the interior angles of a triangle is 180 degrees

Corollary 5.2

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

Reflexive Property

Triangle ABC is congruent to Triangle ABC // Angle B is congruent to Angle B

congruent polygons

all the parts of one polygon are congruent to the corresponding parts

remote interior angles

each exterior angle of a triangle has two of these that are not adjacent to the exterior angle

exterior angles

formed by one side of the triangle and the extension of an adjacent side

congruent segments

line segments that have the same length

corresponding parts

matching parts, of another polygon

Leg

one of its sides, the other two straight lines

Hypotenuse

the longest side of the triangle, and also the one opposite of the right angle

Principle of Superposition

two figures are congruent if and only if there is a rigid motion or series of rigid motions that maps one figure exactly onto the other