EVALUATE Independent Practice Lesson 7.3 Homework ☐ Complete problems 1-8 below for independent practice. When you are finished, check the solutions with your teacher. 1. Order the sides from shortest to longest. S 100° 50° 30° R Q 2. Order the sides from shortest to longest. L 97° 28° 55° K J 3. Order the angles from least to greatest. L 6 9 K M 12 4. Order the angles from least to greatest. S 17 8 T R 16 5. State if the following measures can be the sides of a triangle. 12, 6, 13 6. State if the following measures can be the sides of a triangle. 9, 18, 9 7. State if the following measures can be the sides of a triangle. 8, 3, 6 8. State if the following measures can be the sides of a triangle. 11, 7, 20

Answer:

1. \( \overline{RQ}, \overline{SQ}, \overline{RS} \)
2. \( \overline{KJ}, \overline{LJ}, \overline{LK} \)
3. \( \angle K, \angle L, \angle M \)
4. \( \angle R, \angle T, \angle S \)
5. Yes
6. No
7. No
8. No

Explanation:

1. Triangle Inequality Theorem: The side opposite the smallest angle is the shortest, and the side opposite the largest angle is the longest.
2. Triangle Inequality Theorem: Same principle as above.
3. Triangle Inequality Theorem: The smallest angle is opposite the shortest side.
4. Triangle Inequality Theorem: Same principle as above.

5-8. Triangle Inequality Theorem: For any three sides to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Steps:

1. Order the sides from shortest to longest:

• Given angles: \( \angle R = 50^\circ, \angle S = 100^\circ, \angle Q = 30^\circ \).
• Shortest side opposite smallest angle: \( \overline{RQ} \).
• Longest side opposite largest angle: \( \overline{RS} \).
• Order: \( \overline{RQ}, \overline{SQ}, \overline{RS} \).

1. Order the sides from shortest to longest:

• Given angles: \( \angle L = 97^\circ, \angle J = 28^\circ, \angle K = 55^\circ \).
• Shortest side opposite smallest angle: \( \overline{KJ} \).
• Longest side opposite largest angle: \( \overline{LK} \).
• Order: \( \overline{KJ}, \overline{LJ}, \overline{LK} \).

1. Order the angles from least to greatest:

• Given sides: \( \overline{KL} = 6, \overline{LM} = 9, \overline{KM} = 12 \).
• Smallest angle opposite shortest side: \( \angle K \).
• Largest angle opposite longest side: \( \angle M \).
• Order: \( \angle K, \angle L, \angle M \).

1. Order the angles from least to greatest:

• Given sides: \( \overline{TR} = 8, \overline{RS} = 17, \overline{TS} = 16 \).
• Smallest angle opposite shortest side: \( \angle R \).
• Largest angle opposite longest side: \( \angle S \).
• Order: \( \angle R, \angle T, \angle S \).

1. Check if sides can form a triangle:

• Sides: 12, 6, 13.
• Check: \( 12 + 6 > 13 \), \( 12 + 13 > 6 \), \( 6 + 13 > 12 \).
• All conditions satisfied: Yes.

1. Check if sides can form a triangle:

• Sides: 9, 18, 9.
• Check: \( 9 + 9 > 18 \) (not satisfied).
• Not a triangle: No.

1. Check if sides can form a triangle:

• Sides: 8, 3, 6.
• Check: \( 3 + 6 > 8 \) (not satisfied).
• Not a triangle: No.

1. Check if sides can form a triangle:

• Sides: 11, 7, 20.
• Check: \( 11 + 7 > 20 \) (not satisfied).
• Not a triangle: No.