CK-12 Geometry Concepts

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

TABLE4.9:

Statement Reason

1.AB∼=DC,BE∼=CE 1. Given

2.^6 AEB∼=^6 DEC 2. Vertical Angle Theorem
3. 4 ABE∼= 4 ACE 3. SAS postulate

Practice

Are the pairs of triangles congruent? If so, write the congruence statement and why.

11.

12.

13.

State the additional piece of information needed to show that each pair of triangles is congruent.

4. Use SAS


5. Use SAS


6. Use SAS

Complete the proofs below.

7.Given:Bis a midpoint ofDCAB⊥DCProve: 4 ABD∼= 4 ABC

8.Given:ABis an angle bisector of^6 DACAD∼=ACProve: 4 ABD∼= 4 ABC

9.Given:Bis the midpoint ofDEandAC^6 ABEis a right angleProve: 4 ABE∼= 4 CBD

10.Given:DBis the angle bisector of^6 ADCAD∼=DCProve: 4 ABD∼= 4 CBD

For each pair of triangles, write what needs to be congruent in order for the triangles to be congruent by SAS. Then,
write the congruence statement for the triangles.

1.

2.

3.

4.

5.