If Triangle ABC is congruent to Triangle DEF, What do you know?
1. Angle A is congruent to Angle D.
2. Angle B is congruent to Angle E.
3. Angle C is congruent to Angle F.
4. Segment AB is congruent to Segment DE.
5. Segment BC is congruent to Segment EF.
6. Segment AC is congruent to Segment DF.
CPCTC: Corresponding Parts of Congruent Triangles are Congruent.
Example 1
Given: Ray DB bisects angle ADC, Segment BA is perpendicular to Ray DA, Segment BC is perpendicular to Ray DC.
Prove: Segment BA is congruent to Segment BC.
Statement
1. Ray DB bisects angle ADC, Segment BA is perpendicular to ray DA, Segmen tBC is perpendicular to Ray DC.
2. Angle ADB is congruent to angle CDB.
3. Angle BAD and Angle BCD are Right Angles.
4. Segment BD is congruent to Segment BD.
5. Angle BAd is congruent to Angle BCD.
6. Triangle ABD is congruent to Triangle CBD.
7. Segment BA is congruent to Segment BC.
Reason
1. Given
2. Definition of Angle Bisector
3. Definition of Perpendicular Lines
4. Reflexive
5. All right angles are congruent
6. AAS
7. CPCTC
What did you have to prove for the example?