Geometry Unit 5 Congruent Triangles

Which is NOT a test to prove triangles congruent?

• SAA
• SSS
• SSA
• SAS

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.

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 all four triangles are congruent.

Define: Side-Angle-Side (SAS)

• Not here

• 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.

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.

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

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

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

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

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

Which of the following can not be used to prove that two triangles are congruent?

• Angle-Angle-Side (AAS)
• Side-Angle-Side (SAS) 
• Angle-Angle-Angle (AAA)
• Side-Side-Side (SSS)

Is Angle-Angle-Angle (AAA), a valid rule for proving triangles congruent?

• No
• Sometimes
• Yes
• N/A

If AD bisects <EDI, then

• <ADE=<IDA
• IA=AE
• ID=ED
• All of the above

If DA is perpendicular to IE, then we can immediately conclude that

• IA=AE
• <IAD = <DAE
• <IDA=<EDA
• <IAD and <DAE are right angles