CK-12 Geometry - Second Edition

4.4. Triangle Congruence Using ASA, AAS, and HL http://www.ck12.org

Given:AB||ED,^6 C∼=^6 F,AB∼=ED

Prove:AF∼=CD

Solution:

TABLE4.14:

Statement Reason

1.AB||ED,^6 C∼=^6 F,AB∼=ED Given

2.^6 ABE∼=^6 DEB Alternate Interior Angles Theorem
3. 4 ABF∼= 4 DEC ASA
4.AF∼=CD CPCTC

Example 8:Write a 2-column proof.

Given:Tis the midpoint ofWUandSV

Prove:W S||V U

Solution:

TABLE4.15:

Statement Reason

1.Tis the midpoint ofWUandSV Given

2.W T∼=T U,ST∼=T V Definition of a midpoint

3.^6 ST W∼=^6 U T V Vertical Angle Theorem
4. 4 ST W∼= 4 V T U SAS
5.^6 S∼=^6 V CPCTC
6.W S||V U Converse of the Alternate Interior Angles Theorem

Prove Move: At the beginning of this chapter we introduced CPCTC. Now, it can be used in a proof once two
triangles are proved congruent. It is used to prove the parts of congruent triangles are congruent in order to prove