CK-12 Geometry Concepts

4.6. SSS Triangle Congruence http://www.ck12.org

DF=

√

( 3 − 10 )^2 +( 9 − 7 )^2

=

√

(− 7 )^2 +( 2 )^2

=

√

49 + 4

=

√

53

No sides have equal measures, so the triangles are not congruent.

TABLE4.5:

Statement Reason

1.AB∼=DC,AC∼=DB 1. Given

2.BC∼=CB 2. Reflexive PoC

3. 4 ABC∼= 4 DCB 3. SSS Postulate


4. The triangles are congruent because they have three pairs of sides congruent. 4 DEF∼= 4 IGH.

Practice

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

1.

2.

3.

4.

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

5. Use SSS


6. Use SSS

Fill in the blanks in the proofs below.

7.Given:Bis the midpoint ofDCAD∼=ACProve: 4 ABD∼= 4 ABC

TABLE4.6:

Statement Reason

1. 
   
   
   
   1. 
      
   
   
   
   


2. 
   
   
   
   2. Definition of a Midpoint
   
   
   
   


3. 
   
   
   
   3. Reflexive PoC
   
   
   
   


4. 4 ABD∼= 4 ABC 4.

Find the lengths of the sides of each triangle to see if the two triangles are congruent.

8.

9.