Page 143 - Math Course 2 (Book 2)

Inequalities: Two Triangles

Prove Triangle Relationships
Proof:
Example Statements Reasons

1. E is the midpoint Given
of CB.
Given: ST = PQ SR = QR 2. CE = BE Definition of midpoint
2
ST = SP
3 3. AE = AE Reflexive Property
Prove: m∠SRP > m∠PRQ

Q 4. m∠1 < m∠3 Given
R 5. ∠2 ≅ ∠3 Vertical Angle Theorem
Definition of congruent
6. m∠2 = m∠3 angles
T P
S 7. m∠1 < m∠2 Substitution

8. AC < AB
Proof:
Statements Reasons A. SSS Inequality Theorem
B. SAS Inequality Theorem
C. Substitution
1. SQ = QR Given D. none of the above

2. PR = PR Reflexive Property Answer

3. ST = PQ Given
2
4. ST = SP; SP > ST Given Prove Triangle Relationships
3
5. SP > PQ Substitution Which reason correctly completes the following

6. m∠SRP > m∠PRQ SSS Inequality proof?
Given: X is the midpoint of MB
ΔMCX is isosceles

Your Turn! CB > CM
Prove: m∠CXB > m∠CMX
Use SAS Inequality in a Proof

Which reason correctly completes the two-column C
proof?

Given: m∠1 < m∠3
E is the midpoint of

Prove: AC < AB
A B

M
2 X
1 E B
3

C D

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