Proving

1
Proving

• What are the 5 methods used to prove

SSS
SAS
ASA
AAS
HL
2
RememberA.S.S.is not used to prove congruent
triangles!
3
Popular Terms

• Segment Bisector
• Midpoint
• Angle Bisector
• Vertical Angles
• Perpendicular Lines
• Right Angles
• Reflexive Property

4

• Corresponding parts of congruent triangles are
  congruent
• Isosceles Triangle Theorem
• Converse of the Isosceles Triangle Theorem
• HL

5
Segment Bisector

• A segment bisector divides a segment at its
  midpoint.

A
C
D
E
B
E is the midpoint of
6
Midpoint

• A midpoint divides a segment into two congruent
  segments.

A
B
C
C is the midpoint of AB
7
Angle Bisector

• An angle bisector divides an angle into two
  congruent angles.

A
D
BD bisects
B
C
8
Vertical Angles

• If two angles are vertical angles, then they are
  congruent.

A
C
E
( )
B
D
9
Perpendicular Lines

• Perpendicular lines intersect to form right
  angles.

A
1
2
C
D
3
4
are right angles
B
10
Right Angles

• If two angles are right angles, then they are
  congruent.

A
1
2
C
D
B
11
Reflexive Property

• This is mainly used when you have an angle or
  segment that is a part of 2 different triangles.

A
C
D
B
12
Corresponding Parts of Congruent Triangles are
Congruent
A
A
C
B
B
C
This can only be used once you have proven
congruent triangles!
13
Isosceles Triangle Theorem

• If two sides of a triangle are congruent, then
  the angles opposite those sides are congruent.

B
)
(
C
A
14
Converse of the Isosceles Triangle Theorem

• If two angles of a triangle are congruent, then
  the sides opposite those angles are congruent.

B
)
(
)
(
)
(
)
C
A
A
A
C
A
15
Hypotenuse Leg

• When proving two congruent triangles using HL,
  make sure you have the following
• 1) Right angles
• 2) Right Triangles
• 3) Hypotenuse
• 4) Leg