Using Congruent TrianglesClass Worksheet Part 2

Helpful Information• Deducing information about segments and

angles AFTER proving that the two triangles are congruent. • Sometimes it will be helpful to plan the

proof before you get started.• Remember to start with the 3-2-3.• CPCTC always follows 2 congruent

triangles.• Start at the ends and fill in the middle last.

Popular Reasons in a Proof• Definition of a midpoint

• Two Congruent Segments• Definition of a bisector (or angle bisector)

• Two Congruent Segments (or angles)• Reflexive Property

• Shared segments• Transitive Property

• If a = b and b = c, then a = c.• Symmetric Property

• If a = b, then b = a.

More Popular Reasons…

• Parallel Lines • Alternate Interior Angles• Corresponding Angles• Same Side Interior Angles

• Vertical Angles • Methods of Congruence

• SSS, SAS, ASA, AAS or HL

Complete the following proof:Statements Reasons

1. 1. Given

2. BD=BD 2.

3. ∆BDA = ∆BDC 3.

4. DA=DC 4.

5. D is the midpoint of AC

5.

6. 6. Def. of a seg. Bis.

Complete the following proof:Statements Reasons

1. AB=DC; AD=BC 1. Given

2. 2.

3. 3.

4. 4.

5. 5.

6. AB is parallel to DC

6.

Complete the following proof:Statements Reasons

1. Given

2. TQ=TQ 2.

3. ∆RQT = ∆SQT 3.

4. <RQT=<SQT 4.

5. 5.

Complete the following proof:Statements Reasons

1. AD=CD; DB bisects <CDA

1. Given

2. 2.

3. 3.

4. 4.

5. 5.

6. AC is perpendicular to BD

6.

Complete the following proof:

Statements Reasons

1. AB is parallel to PQ; AB=PQ

1. Given

2. 2.

3. 3.

4. 4.

5. BZ = ZQ 5.

Complete the following proof:

Statements Reasons

1. BC=DC; <3=<4 1. Given

2. 2.

3. 3.

4. 4.

5. AC bisect <BAD 5.