Geometry Topic 4

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 __ by ASA (Angle-Side-Angle) Congruence Postulate.

congruent

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent by __.

SSS (Side-Side-Side) Congruence Postulate.

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent by __.

SAS (Side-Angle-Side) Congruence Postulate.

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 by __.

ASA (Angle-Side-Angle) Congruence Postulate.

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

AAS (Angle-Angle-Side) Congruence Theorem.

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

HL (Hypotenuse-Leg) Congruence Theorem.

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent by ****__.

SSS (Side-Side-Side) Congruence Postulate.

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 by ****__.

ASA (Angle-Side-Angle) Congruence Postulate.

If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent by ****__.

AAS (Angle-Angle-Side) Congruence Theorem.

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent by ****__.

HL (Hypotenuse-Leg) Congruence Theorem.

To prove triangles congruent using SSS, one must show that all three corresponding ____ are congruent.

sides

When constructing a congruence proof using SAS, you must ensure the congruent angle is the two congruent sides.

included between

The Reflexive Property of congruence states that any geometric figure is congruent to ____.

itself

A common reason used in congruence proofs when two lines intersect is that angles are congruent.

vertical

In a geometric proof, statements are accompanied by that justify each step.

reasons

To use the HL Theorem, both triangles must first be established as triangles.

right