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.

   Esme plans a kite wing: one angle of 30°, the 12 cm side next to it, and the 4 cm side across from it. Which describes the triangles Esme can draw?

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

   Kira sketches a ramp side: one angle of 30°, the 8 cm side next to it, and the 11 cm side across from it. Which describes the triangles Kira can draw?

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

   Luz sketches a toy boat sail: one angle of 30°, the 16 cm side next to it, and the 5 cm side across from it. Which describes the triangles Luz 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.

   Ren has two paper strips, 6 cm and 9 cm, for two sides of a triangle. The third side is a whole number of centimeters. How many different lengths could it be?

   11
6. 6.

   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
7. 7.

   Ari draws a kite wing with one angle of 40°. A second angle is a whole number of degrees. What is the largest that second angle can be, in degrees?

   139

8. Read this first

   Use this

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

9. 8.

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

   • Two angles of 105° and 90° and the 6 cm side between them
   • Angles of 45°, 55° and 80°
   • Two angles of 52° and 61° and the 9 cm side between them
10. 9.

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

    • Angles of 30°, 60° and 90°
    • Sides of 6 cm, 7 cm and 9 cm
    • Two angles of 62° and 48° and the 8 cm side between them
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