Proof – A logical argument that shows a statement is true
Theorem – A statement that has been formally proven
Theorem 2.1: Segments congruence is reflexive, symmetric, and transitive.
Reflexive property of
≅
: For any segment
AB
, ________________.
Examples
: (a)
JK
≅
_______ (b)
XY
≅
_______
Symmetric property of
≅
: If
CD
AB ≅
, then ___________________.
Example
: (a) If
GH WO≅
, then _________________
(b) If
JK LM≅
, then _________________
Transitive property of
≅
: If
CDAB ≅
and
EFCD ≅
, then _________________.
Example
: (a) If
JK LM≅
and
LM HA≅
, then _________________
(b) If
XY SU
≅
and
SU TK≅
, then _________________
Theorem 2.2: Angle congruence is reflexive, symmetric, and transitive.
Reflexive property of
≅
: For any angle A, ______________.
Examples
: (a)
K
∠
≅
_______ (b)
Y∠
≅
_______
Symmetric property of
≅
: If
∠
A
≅
∠
B, then _________________.
Example
: (a) If
GH∠ ≅∠
, then _________________
(b) If
LMN RST∠ ≅∠
, then _________________
Transitive property of
≅
: If
∠
A
≅
∠
B and
∠
B
≅
∠
C, then __________________.
Example
: (a) If
JZ∠ ≅∠
and
ZH∠ ≅∠
, then _________________
(b) If
YAB LOG∠ ≅∠
and
LOG UVT∠ ≅∠
, then ____________________
A two-column geometric proof consists of a list of
statements
, and the
reasons
to show that
those statements are true.
1. Read the given(s) and what is to be proved. This is the beginning and end to the proof.
2. Draw a figure that illustrates what is to be proved, if one is not already given.
3. Mark the figure according to what you can deduce about it from the information given.
4. Write the steps down carefully, without skipping even the simplest one, and be sure to
number each step.
