Prove Statements about
Segments and Angles
Day 2
Lesson 4.5
Page 217
The goal of this lesson is be able to
write proofs using geometric theorems.
Vocabulary:
1. A proof is a logical argument that shows a
statement is true.
2. A postulate is a rule that is accepted without
proof.
3. A theorem is a statement that can be proven.
4. Segment Addition Postulate
If B is between A
and C, then AB +
BC = AC.
AB = 2.81 cm
BC = 3.54 cm
If AB + BC =
AC, then B is
between A and C.
AC = 6.35 cm
A
AB+BC = 6.35 cm
B
C
5. Angle Addition Postulate
If P is in the interior of RST ,
then the measure of RST is
equal to the sum of the measures
of RSP and PST .
mRST = 68.00
mRSP = 30.04
mPST = 37.96
mRSP+mPST = 68.00
R
P
S
T
Given:
m1 = m4,
mEHF = 90
mGHF = 90
F
2
Prove:
m2 = m3
1
E
Statements
m1 = m4,
mEHF = 90
mGHF = 90
2 mEHF = mGHF
1
3
4
mEHF = m1 + m2
mGHF = m3 + m4
3
4
H
G
Reasons
1
Given
2 Substitution Property of Equality
3
Angle Addition Postulate
4
Substitution Property of Equality
5
Substitution Property of Equality
6
Subtraction Property of Equality
m1 + m2 = m3 + m4
5
m1 + m2 = m3 + m1
6
m2 = m3
Theorem 4.1 Congruence of Segments
• Reflexive
For any segment AB, AB  AB
• Symmetric
If AB  CD then CD  AB
• Transitive
If AB  CD and CD  EF, then AB  EF
Theorem 4.2 Congruence of Angles
• Reflexive
For any angle A, A  A.
• Symmetric
If A  B, then B  A.
• Transitive
If A  B and B  C, then A  C.
Homework Assignment
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