Subscribe

7th grade · Math · Unit 18 of 20

One Triangle, Many or None?

Sides and angles that make triangles

What your child practices

Deciding whether given sides and angles make exactly one triangle, more than one, or none: the two shorter sides must add to more than the longest, the angles must add to 180°, and three angles fix the shape but not the size.

New York State Learning Standards learning standard: NY-7.G.2 · drawing triangles from given angles and sides, and noticing when the conditions make one triangle, more than one, or none

How we explain it

Children can open this short lesson before they practice.

  1. Three sides make a triangle only if the two shorter sides add to more than the longest.
  2. The three angles of a triangle always add to 180°.
  3. Three sides fix exactly one triangle. Three angles fix the shape but not the size, so many triangles fit.

Example: Can sides of 4 cm, 5 cm and 10 cm make a triangle? The two shorter sides add to 4 + 5 = 9. 9 is less than 10, so the short sides cannot meet. Answer: No triangle

One Triangle, Many or None? in New York

In the New York State Learning Standards, this is unit 18 of 20 in 7th grade Math, after Rewriting Expressions and before Slicing Solids.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: New York State Education Department (NYSED)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    Two sides of a triangle are 9 m and 4 m. Which could be the third side?

    • 11 m
    • 14 m
    • 4 m
    • 18 m

  2. Question 2

    Can a triangle have two right angles?

    • No: two 90° angles already make 180°
    • Yes, if it is big
    • No: right angles are not allowed
    • Yes, any triangle can

  3. Question 3

    How many triangles can you draw with sides of 3 cm, 3 cm and 3 cm?

    • exactly one triangle
    • more than one triangle
    • no triangle

  4. Question 4

    How many triangles have sides of 10 cm and 4 cm with a 65° angle between them?

    • more than one triangle
    • no triangle
    • exactly one triangle

  5. Question 5

    How many triangles can you draw with sides of 10 cm, 5 cm and 16 cm?

    • exactly one triangle
    • more than one triangle
    • no triangle

  6. Question 6

    How many triangles can you draw with angles of 20°, 25° and 125°?

    • more than one triangle
    • no triangle
    • exactly one triangle

More 7th grade