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Right Triangle Identification

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Right Triangle Identification

Help the design team check triangle shapes for a new skate park. A right triangle has one 90° angle. The two sides that meet at that angle are the legs; the remaining side is the hypotenuse. Show your reasoning where asked.

Spot the right triangles

Use the angle information in each design to decide whether it contains a right triangle.

1.A triangular ramp has angles measuring 90°, 35°, and 55°. Is it a right triangle? Explain using its angles.
2.Which set of angle measures describes a right triangle?
  • 40°, 50°, 90°
  • 60°, 60°, 60°
  • 30°, 60°, 80°
  • 45°, 45°, 45°
3.A blueprint shows a triangle with a small square at one corner. What does that square tell the builder?
4.A small square is drawn at one corner of a triangle on a design. What does this symbol indicate about the angle at that corner?

Name the sides

In every right triangle, the side opposite the right angle is the hypotenuse. The other two sides are the legs.

5.A right triangle has legs measuring 6 inches and 8 inches. Which side is the hypotenuse: the side opposite the 90° angle, or a side that forms the 90° angle?
  • The side opposite the 90° angle
  • A side that forms the 90° angle
  • Either side could be the hypotenuse
6.Draw a right triangle in the box. Mark the 90° angle with a small square, then label both legs and the hypotenuse.
7.A triangle has side lengths 5 cm, 12 cm, and 13 cm. The longest side is opposite the largest angle. Which side would be the hypotenuse if this triangle is a right triangle?
8.True or false: Every triangle has a hypotenuse. Explain your choice.

Check the design

Use what you know about right triangles to evaluate the skate park plans.

9.The design team needs a triangular brace with a right angle. The listed angles are 42° and 48°. What must the third angle be, and does the brace qualify as a right triangle?
10.A designer claims a triangle with side lengths 7 ft, 9 ft, and 12 ft must be a right triangle because 12 ft is the longest side. Is that enough evidence? Explain how the designer could check using the side lengths.

3 printable pages

  • Right Triangle Identification, page 1 of 3: Spot the right triangles

    Page 1

  • Right Triangle Identification, page 2 of 3: Name the sides

    Page 2

  • Right Triangle Identification, page 3 of 3: Check the design

    Page 3

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