Exploring Triangle Congruence and Geometric Proofs

What is the purpose of a geometric proof in geometry?

• To measure angles and sides

• To draw accurate diagrams

• To guess the properties of shapes

• To show something is true by justifying each step

In a two-column proof, what is written in the right-hand column?

• Reasons for each step

• Diagrams

• Conclusions

• Statements

What is the first step in writing a triangle congruence proof?

• Identify the postulates

• Mark any given information

• Draw the diagram

• Write the conclusion

Which postulate is used to prove that triangle BCA is congruent to triangle DCE in the example?

• Side-Side-Side

• Side-Angle-Side

• Angle-Side-Angle

• Angle-Angle-Side

What does the reflexive property state?

• All right angles are congruent

• A segment is congruent to itself

• Vertical angles are congruent

• Alternate interior angles are congruent

In the example with angle G and angle I, what does segment FH do?

• It is congruent to itself

• It is parallel to GI

• It bisects angle GFI

• It is perpendicular to GF

What is the definition of perpendicular lines?

• Lines that never meet

• Lines that are congruent

• Lines that form right angles

• Lines that bisect each other

What does CPCTC stand for?

• Congruent Parts of Congruent Triangles are Congruent

• Congruent Parts of Corresponding Triangles are Congruent

• Corresponding Parts of Congruent Triangles are Corresponding

• Corresponding Parts of Congruent Triangles are Congruent

Which angles are congruent due to alternate interior angles in the final example?

• Angle DAC and angle BAC

• Angle BCA and angle DCA

• Angle BAC and angle DCA

• Angle DAC and angle BCA

What is the final conclusion of the proof involving CPCTC?

• Segment AB is congruent to segment CD

• Angle B is congruent to angle D

• Segment BC is congruent to segment AD

• Triangle BAC is congruent to triangle DCA