Virginia SOL 8.MG.4

8.MG.4 is a Standards of Learning standard. These are the knowledge and skills expectations under it.

• 8.MG.4.a

  Verify the Pythagorean Theorem using diagrams, concrete materials, and measurement.

• 8.MG.4.b

  Determine whether a triangle is a right triangle given the measures of its three sides.

• 8.MG.4.c

  Identify the parts of a right triangle (the hypotenuse and the legs) given figures in various orientations.

• 8.MG.4.d

  Determine the measure of a side of a right triangle, given the measures of the other two sides.

• 8.MG.4.e

  Apply the Pythagorean Theorem, and its converse, to solve problems involving right triangles in context.

01

What Students Need to Do

Students identify the legs and hypotenuse of a right triangle in any position. They use side lengths to find a missing length or decide whether a triangle is right. They confirm the side-length relationship with diagrams, tiles, or measurements and solve practical problems.

02

What Mastery Looks Like

Students correctly label the legs and hypotenuse, even when a triangle is rotated. They find missing side lengths and show squared values, subtraction or addition, and the square root. They also test three side lengths and explain what the result means in context.

03

Common Misconceptions

Students may label the longest-looking side as the hypotenuse instead of finding the side opposite the right angle. They may add squares when finding a leg, forget the square root, or round too early. When testing three sides, they may not use the longest side as c.

04

How to Assess It

Exit ticket: Decide whether side lengths 8, 15, and 17 form a right triangle and show your work. Then find the missing leg when the hypotenuse is 13 and the other leg is 5.

1. 01

   Build a 3-4-5 triangle with craft sticks, then use grid-paper squares on each side to compare their areas.

2. 02

   Explain in writing why the side opposite the right angle must be c before substituting into a² + b² = c².

3. 03

   Play a card sort matching side-length triples to right triangle, not right triangle, and missing-side solution cards.

4. 04

   Find the diagonal brace length needed for a rectangular gate measuring 6 feet by 8 feet.

• 6.MG.2

  The student will reason mathematically to solve problems, including those in context, that involve the area and perimeter of triangles and parallelograms.

• 6.MG.2.b

  Solve problems, including those in context, involving the perimeter and area of triangles and parallelograms.

• 5.MG.3

  The student will classify and measure angles and triangles, and solve problems, including those in context.