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