CK-12 Geometry Concepts

4.8. ASA and AAS Triangle Congruence http://www.ck12.org

Practice

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.

3.

For questions 4-8, use the picture and the given information below.

Given:DB⊥AC,DBis the angle bisector of^6 CDA

4. FromDB⊥AC, which angles are congruent and why?


5. BecauseDBis the angle bisector of^6 CDA, what two angles are congruent?


6. From looking at the picture, what additional piece of information are you given? Is this enough to prove the
   two triangles are congruent?


7. Write a two-column proof to prove 4 CDB∼= 4 ADB, using #4-6.


8. What would be your reason for^6 C∼=^6 A?

For questions 9-13, use the picture and the given information.

Given:LP||NO,LP∼=NO

9. FromLP||NO, which angles are congruent and why?


10. From looking at the picture, what additional piece of information can you conclude?


11. Write a two-column proof to prove 4 LMP∼= 4 OMN.


12. What would be your reason forLM∼=MO?


13. Fill in the blanks for the proof below. Use the given from above.Prove:Mis the midpoint ofPN.

TABLE4.14:

Statement Reason

1.LP||NO,LP∼=NO 1. Given

2. 
   
   
   
   2. Alternate Interior Angles
   
   
   
   


3. 
   
   
   
   3. ASA
      4.LM∼=MO 4.
      5.Mis the midpoint ofPN. 5.
   
   
   
   

Determine the additional piece of information needed to show the two triangles are congruent by the given postulate.

14. AAS


15. ASA


16. ASA


17. AAS