2.6 Prove Statements about Segments and
Angles
The reasons used to justify your steps in solving a problem or in making a convincing argument can include:
_________________________, _________________________, _________________________,
and ___________________________. A theorem is a statement that can be proven; and once proven,
it can be used as justifications in your arguments. The following theorems are easily proven.
Congruence of Segment is:
Reflexive: For any segment AB,
Symmetric: If
, then
Transitive: If
and
, then
Congruence of Angles is:
Reflexive: For any angle A, A A
Symmetric: If A B, then B A
Transitive: If A B and B C, then A
C
Example 1: Name the theorem that the statement illustrates.
a. If GH  JK, then JK  GH.
b. DE  DE
c. If P  Q and Q  R, then P  R.
Example 2: Complete each statement and justify using the new theorems.
a. TPQ  ______
b. If 1  2, then ________
c. If PQ  AB and _____________, then PQ  XY.
Example 3: Use the diagram to prove AC = AB + AB.
Given: BC = AB
Prove: AC = AB + AB
Statements
1.BC = AB
Reasons
1. Given
2.
2.
3.
3.
2.6 Prove Statements about Segments and
Angles
Example 4: Use the diagram to prove m1 = m4.
Given: m2 = m3, mAXC = mAXD
Prove: m1 = m4
Statements
Reasons
1.
2.
3.
4.
5.
Example 5: If you know that BD bisects ABC, prove that mABC is two times ml.
Given BD bisects ABC Prove mABC = 2  ml
Statements
Reasons
1. BD bisects ABC.
1.
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.