Lesson 11-1: Use Side Lengths and Angle Measures to Draw and Analyze Triangles — Practice Questions

1. 1. A triangle has two sides with lengths 11 and 7. The length of the third side must be greater than ___.

2. 2. Two sides of a triangle measure 9 units and 15 units. The length of the third side must be less than ___.

3. 3. Two sides of a triangle have lengths of 6 cm and 17 cm. Which of the following could be the length of the third side?

   • A. 10 cm
   • B. 23 cm
   • C. 11 cm
   • D. 19 cm

4. 4. A triangle has two sides of length 20. If $c$ is the length of the third side, which inequality represents the possible values of $c$?

   • A. $0 < c < 20$
   • B. $0 < c < 40$
   • C. $1 \leq c \leq 39$
   • D. $0 \leq c \leq 40$

5. 5. A triangle has side lengths of 4 inches and 9 inches. Which of the following could NOT be the length of the third side?

   • A. 6 inches
   • B. 13 inches
   • C. 8 inches
   • D. 11 inches

6. 6. Why does the Angle-Angle-Angle (AAA) condition not guarantee a unique triangle?

   • A. The angles might be in a different order.
   • B. The side lengths are not specified, so the triangle's size can vary.
   • C. The sum of the angles might not be $180^\circ$.
   • D. It is impossible to draw a triangle given only angles.

7. 7. A designer is creating a triangular logo with angles measuring $45^\circ$, $55^\circ$, and $80^\circ$. How many different triangles can be created with these specific angles?

   • A. Exactly one
   • B. Exactly two
   • C. Infinitely many
   • D. None

8. 8. A unique triangle is a single, specific triangle defined by a set of conditions. Given only the angle measures $25^\circ, 65^\circ,$ and $90^\circ$, how many *unique* triangles can be constructed? ___

9. 9. Which statement best explains why knowing only the angles $50^\circ, 50^\circ,$ and $80^\circ$ is not enough to define a single, unique triangle?

   • A. The angles determine the shape but not the size.
   • B. The angles must all be different.
   • C. The triangle must be a right triangle.
   • D. The sum of the angles is not $180^\circ$.

10. 10. Consider the statement: "Any two triangles with angle measures of $40^\circ, 60^\circ,$ and $80^\circ$ must be identical in size and shape." Is this statement correct?

    • A. Yes, because the angles are the same.
    • B. No, because they could have different sizes.