6th Grade Math Textbook, Fundamentals

Determine whether a triangle with the given side lengths is a right triangle.

1.14 cm, 15 cm, 16 cm 2.30 in., 40 in., 50 in. 3.3.5m, 12 m, 12.5 m

Suppose that aand bare the lengths of the legs of a right triangle and that cis
the length of the hypotenuse. Find the length of the missing side to the nearest
tenth. You may use a calculator.

4.a16 km, b63 km 5.b100 in., c150 in. 6.a13 miles, c17 miles

7.Discuss and Write When each leg of a right triangle is doubled in length,

what happens to the length of the hypotenuse? Is this always true? Explain.

Lesson 10-5 for exercise sets. &KDSWHU 

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You can use the Pythagorean Theorem equation to decide whether

or not a given triangle is a right triangle. You can use a calculator to

verify whether or not the equation a^2 b^2 c^2 is true for the side

lengths a, b,and cof a given triangle.

You can apply the Pythagorean Theorem to find the length of a line

shown on a grid.

Find the length of the red line segment on the grid at the right.

Assume that the side of each small square on the grid is 1 unit.

Each group of three numbers that can form the side lengths of a right

triangle is called a. Common Pythagorean triples

are 3-4-5, 5-12-13, and 8-15-17. Multiples of these triples are also

Pythagorean triples. For example, 3, 4, and 5 can each be multiplied

by 3 to produce another Pythagorean triple, 9-12-15.

Pythagorean triple

Draw a vertical line segment from the upper endpoint of the

red line segment straight down to the horizontal grid line that

aligns with the other endpoint of the red line segment.

Draw a horizontal line segment that connects the vertical line

segment to the red line segment. The corner of the grid box will

help you form a right angle.

Since you have constructed a right triangle, you can now use

the Pythagorean Theorem to find the length of the hypotenuse

(the red line segment). Count units to determine the lengths

of the legs as 6 units and 8 units.

a^2 b^2 c^2 Pythagorean Theorem

62  82 c^2 Substitute 6 and 8 for aand b.

36  64 c^2 Evaluate the squares.

100 c^2 Find the sum.

 Find the positive square root of both sides.

10 c Simplify.

So the length of the red line segment is 10 units.

100 c^2