CK-12 Geometry-Concepts

http://www.ck12.org Chapter 4. Triangles and Congruence

Given:AB||ED,^6 C∼=^6 F,AB∼=ED

Prove:AF∼=CD

Answers:

1. Even thoughKL∼=ST, they are not corresponding. Look at the angles aroundKL,^6 Kand^6 L.^6 Khasonearc
   and^6 Lis unmarked. The angles aroundSTare^6 Sand^6 T.^6 Shastwoarcs and^6 Tis unmarked. In order to use
   AAS,^6 Sneeds to be congruent to^6 K. They are not congruent because the arcs marks are different. Therefore, we
   cannot conclude that these two triangles are congruent.


2. Here is the proof:

TABLE4.12:

Statement Reason

1.BDis an angle bisector of^6 CDA,^6 C∼=^6 A Given

2.^6 CDB∼=^6 ADB Definition of an Angle Bisector
3.DB∼=DB Reflexive PoC
3. 4 CBD∼= 4 ABD AAS
3. First, prove that the triangles are congruent. Once you have proved they are congruent, you need one more step
to show that the corresponding pair of sides must be congruent. Remember that CPCTC stands forcorresponding
parts of congruent triangles are congruent.

TABLE4.13:

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

Explore More

For questions 1-3, determine if the triangles are congruent. If they are, write the congruence statement and which
congruence postulate or theorem you used.

1.

2.