Compare m∠5 to m∠2.
By Exterior Angle Theorem:
m∠2 = m∠3 and m∠5
By Exterior Angle Inequality Theorem m∠2 > m∠3 and m∠5
Compare m∠3 to m∠2
By the Exterior Angle Theorem:
m∠1 = m∠4 and m∠5
By Exterior Angle Inequality Theorem m∠1 > m∠4 and m∠5
Compare m∠1 to m∠2
Since all right angles are equal then m∠1 = m∠3 From the statement above
m∠2 > m∠3 and m∠5
By substitution, m∠2 > m∠1 and m∠5 Therefore ∠2 has the greatest measure.
Objective: To illustrate exterior angle inequality theorem of a triangle
1. Determine which angle has the greatest measure.
Examples:
∠1 has the greatest measure.
∠6 has the greatest measure.
2. Determine which angle has the greatest measure.
3. Which of ∠6, ∠3 and ∠4 has the greatest measure?
ACTIVITY
Name: _______________________ Date: ___________ Score: ____________
Answer the following.
1. Which of ∠1, ∠2 and ∠4 has the largest measure?
2. Which of ∠5, ∠3 and ∠2 has the largest measure?
3. Which of ∠2, ∠4 and ∠5 has the largest measure?
4. Which of ∠1, ∠4 and ∠5 has the largest measure?
For numbers 6-10, use the figure below to list all the angles that satisfy the stated condition.
5. Angles whose measures are less than m∠1.
6. Angles whose measures are less than m∠7.
7. Angles whose measures are less than m∠8.
8. Angle/s whose measure/s is/are greater than m∠3.
9. Angle/s whose measure/s is/are greater than m∠4.
10. Angle/s whose measure/s is/are greater than m∠9.
Key to Correction:
1. ∠4 2. ∠5 3. ∠2 4. ∠1
5. ∠3 and ∠6 6. ∠2 and ∠3 7. ∠4 and ∠9 8. ∠1 and ∠7 9. ∠8
10. ∠8