Geometry: Triangle Congruence and Theorems

Practice vocabulary flashcards covering triangle congruence postulates, base angle theorems, equilateral triangle corollaries, and related geometric principles.

$\Delta$ Base Angle Theorem

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

Converse $\Delta$ Base Angle Theorem

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

Equilateral $\Delta$ Corollaries

Corollaries stating that if a triangle is equilateral, then it is equiangular; if a triangle is equiangular, then it is equilateral; and each interior angle measures $60^\circ$.

Side-Side-Side Postulate (SSS)

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

Side-Angle-Side Postulate (SAS)

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

Angle-Side-Angle Postulate (ASA)

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

Angle-Angle-Side Theorem (AAS)

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

AAA and SSA

Angle combinations and side-angle configurations that cannot be used to prove triangle congruence.

Corresponding Parts of Congruent Triangles (CPCTC)

The geometric principle stating that corresponding parts of congruent triangles are congruent.

Congruent $\Delta$ ‘s

Triangles that have the same shape, characterized by corresponding angles that are congruent.

Congruence of Triangles as an Equivalence Relation

The geometric property establishing that triangle congruence satisfies the conditions of an equivalence relation.

Perimeter

The sum of the measures of the side of a polygon

HL Theorem

if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of a second triangle then the triangles are congruent

Concurrent Lines

Lines that have exactly one point in common

∠Bisectors

A line segment of ray that starts at the vertex of a triangle and bisects the angle

Incenter

Point of Concurrency of ∠bisectors that ALWAYS lie INSIDE the triangle

Medians

A segment whose endpoints are a vertex and the midpoint of the opposite side

Centroid

Point of concurrency of medians that ALWAYS lie INSIDE the triangle

Altitudes

A line segment from the vertex to the opposite side (may be extended) that is ⟂

Orthocenter

Point of concurrency of altitudes that may be, INSIDE, ON or OUTSIDE the triangle.

Perpendicular bisectors

A line, segment or ray that is ⟂ to one side of the triangle at the midpoint.

Cicumcenter

The point of concurrency of