Proving Triangle Congruence: SSS and SAS Methods

This video tutorial covers the concept of congruent triangles, focusing on the SSS and SAS postulates. It explains how these postulates serve as shortcuts to prove triangle congruence without needing to verify all six corresponding parts. The tutorial also introduces the concept of proofs in geometry, demonstrating how to use two-column proofs to establish triangle congruence. Advanced topics include the congruent supplement theorem and its application in proving angle congruence. The video aims to provide a comprehensive understanding of congruent triangles and the methods used to prove their congruence.

What must be true for two triangles to be considered congruent?

• All corresponding sides and angles must be equal.

• Only one side must be equal.

• Only one angle must be equal.

• All sides must be equal but angles can differ.

Tags

CCSS.8.G.A.2

What does the SSS postulate state?

• One side and two angles of one triangle are equal to one side and two angles of another triangle.

• Three angles of one triangle are equal to three angles of another triangle.

• Three sides of one triangle are equal to three sides of another triangle.

• Two sides and one angle of one triangle are equal to two sides and one angle of another triangle.

Tags

CCSS.HSG.SRT.B.5

If two triangles have three pairs of equal sides, what can be concluded?

• The triangles are congruent.

• The triangles are similar.

• The triangles are right triangles.

• The triangles are isosceles.

Tags

CCSS.8.G.A.2

What is the included angle in the SAS postulate?

• An angle that is not between the two sides.

• An angle that is outside the triangle.

• An angle that is between the two equal sides.

• Any angle in the triangle.

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Which postulate can be used if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle?

• SSS

• ASA

• SAS

• AAS

Tags

CCSS.HSG.SRT.B.5

What does CPCTC stand for?

• Corresponding Parts of Congruent Triangles are Equal

• Corresponding Parts of Similar Triangles are Congruent

• Corresponding Parts of Congruent Triangles are Congruent

• Corresponding Parts of Similar Triangles are Equal

Tags

CCSS.HSG.SRT.B.5

If two triangles are proven congruent, what can be said about their corresponding parts?

• They are similar.

• They are equal.

• They are proportional.

• They are different.

Tags

CCSS.8.G.A.2

What is the first step in a two-column proof?

• Draw the diagram.

• State the conclusion.

• State the given information.

• List all possible theorems.

What is the purpose of a two-column proof?

• To list all possible solutions.

• To prove a statement using logical steps.

• To measure angles and sides.

• To draw a diagram.

Tags

CCSS.HSG.SRT.B.5

In a two-column proof, what do the columns represent?

• Statements and reasons

• Theorems and postulates

• Diagrams and measurements

• Questions and answers