Page 140 - Math Course 2 (Book 2)

Triangle Inequality Theorem

Your Turn!

Identify Sides of a Triangle Prove Theorem 10.11

Determine whether 6, 9, 16 can be lengths of the Choose the correct reason to complete the
sides of a triangle. following proof.

A. yes Given: AD is an altitude in ΔABC.
B. no Prove: AB > AD
C. cannot be determined
A

Answer

1 2
C D B

Determine whether 14, 16, 27 can be lengths of the Proof:
sides of a triangle. Statements Reasons

A. yes 1. AD is an altitude Given
B. no in △ABC
C. cannot be determined
2. AD ⟂ BC Definition of altitude
Answer
3. ∠1 and ∠2 are Perpendicular lines form
right angles. right angles

All right angles are
4. ∠1 ≅ ∠2
congruent.
Definition of congruent
5. m∠1 = m∠2
angles
Determine Possible Side Lengths
6. m∠1> m∠B 6.
In ΔXYZ, XY = 6, and YZ = 9. Which measure cannot
be XZ?
7. m∠2 > m∠B Substitution
A. 4
B. 9 If an angle of a triangle is
C. 12 greater than a second angle,
D. 16 then the side opposite the
8. AB > AD
Answer greater angle is longer than
the side opposite the lesser
angle

A. Definition of inequality
B. Substitution
C. Triangle Inequality Theorem
D. Exterior Angle Inequality Theorem

Answer

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