Can these sides and angles make a triangle?

Answer Key - Grade 7 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Jun plans a tent end: one angle of 30°, the 10 cm side next to it, and the 7 cm side across from it. Which describes the triangles Jun can draw?

   • More than one triangle: different sizes or shapes fit
   • No triangle: nothing fits
   • Exactly one triangle: only one size and shape fits
2. 2.

   Milo plans a roof end: one angle of 30°, the 14 cm side next to it, and the 9 cm side across from it. Which describes the triangles Milo can draw?

   • Exactly one triangle: only one size and shape fits
   • No triangle: nothing fits
   • More than one triangle: different sizes or shapes fit
3. 3.

   Noah draws a triangle on paper: one angle of 30°, the 6 cm side next to it, and the 9 cm side across from it. Which describes the triangles Noah can draw?

   • No triangle: nothing fits
   • More than one triangle: different sizes or shapes fit
   • Exactly one triangle: only one size and shape fits
4. 4.

   Pia has two pieces of yarn, 5 cm and 12 cm, for two sides of a triangle. The third side is a whole number of centimeters. How many different lengths could it be?

   9
5. 5.

   Tala has two pieces of yarn, 7 cm and 10 cm, for two sides of a triangle. The third side is a whole number of centimeters. How many different lengths could it be?

   13
6. 6.

   Esme draws a toy boat sail with one angle of 25°. A second angle is a whole number of degrees. What is the largest that second angle can be, in degrees?

   154

7. Read this first

   Use this

   Three sets of measures are listed in the choices. No picture is drawn.

8. 7.

   Kira has three sets of measures for a triangle. Which set can build exactly one triangle?

   • Two angles of 52° and 61° and the 9 cm side between them
   • Two angles of 105° and 90° and the 6 cm side between them
   • Angles of 45°, 55° and 80°
9. 8.

   Milo has three sets of measures for a triangle. Which set can build exactly one triangle?

   • Angles of 65°, 50° and 65°
   • Sides of 13 cm, 14 cm and 20 cm
   • Two angles of 96° and 84° and the 10 cm side between them
10. 9.

    Ren has three sets of measures for a triangle. Which set can build more than one triangle?

    • Angles of 50°, 50° and 80°
    • Angles of 60°, 70° and 60°
    • Sides of 10 cm, 11 cm and 15 cm
11. 10.

    Tala has three sets of measures for a triangle. Which set can build more than one triangle?

    • Angles of 70°, 40° and 70°
    • Angles of 80°, 75° and 90°
    • Sides of 14 cm, 15 cm and 30 cm