Identifying Congruent Sides and Angles in Triangles

Define: Base Angles Theorem

• If two sides of a triangle are congruent, then the angles opposite them are congruent.
• If three sides of a triangle are congruent, then the angles opposite them are congruent.
• If one side of a triangle are congruent, then the angles opposite them are congruent.
• If no sides of a triangle are congruent, then the angles opposite them are congruent.

Tags

CCSS.HSG.SRT.B.4

Define: Side-Side-Side (SSS) Congruence Postulate

• 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 two triangles are congruent.
• If two sides of a triangle are congruent, then the angles opposite them are congruent.
• If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.
• 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 two triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Define: Corollary to the Base Angles Theorem

• If two sides of a triangle are congruent, then the angles opposite them are congruent.
• The sum of the measures of the interior angles of a triangle is 180 degrees.
• If a triangle is equiangular, then it is equilateral.
• If a triangle is equilateral, then it is equiangular.

Tags

CCSS.HSG.SRT.B.4

Define: Angle-Angle-Side (AAS) Congruence Theorem

• If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangles, then the three triangles are congruent.
• If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangles, then the two triangles are congruent.
• If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangles, then the single triangle is congruent.
• If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangles, then all four triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

Define: Corollary to the Converse of the Base Angles Theorem

• If a triangle is equilateral, then it is equiangular.
• If a triangle is equiangular, then it is equilateral.
• The sum of the measures of the interior angles of a triangle is 180 degrees.
• The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

Tags

CCSS.8.G.B.8

Define: Side-Angle-Side (SAS) Congruence Postulate

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

Tags

CCSS.HSG.SRT.B.5

Define: Angle-Side-Angle (ASA) Congruence Postulate

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

Tags

CCSS.HSG.SRT.B.5

Define: Congruent Triangles to Prove Corresponding Parts Congruent (CPCTC)

• CTCPC can be used to show corresponding parts of congruent triangles congruent.
• CPCTC can be used to show corresponding parts of congruent triangles congruent.
• CPCTC can be used to show corresponding sides of congruent triangles congruent.
• CPCTC can be used to show corresponding parts of congruent triangles congruent.

Tags

CCSS.HSG.SRT.B.5

Define: Third Angles Theorem

• If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
• If three angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
• If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also similar.
• If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

Tags

CCSS.HSG.CO.B.7

Define: Triangle Sum Theorem

• The sum of the measures of the interior angles of a triangle is 360 degrees.
• The sum of the measures of the interior angles of a triangle is 180 degrees.
• The sum of the measures of the exterior angles of a triangle is 180 degrees.
• The product of the measures of the interior angles of a triangle is 180 degrees.

Tags

CCSS.8.G.A.5