Grade 10 · Math · Geometry

10th grade Acute, right or obtuse from the sides, Pythagorean triples, and 45-45-90 and 30-60-90 triangles worksheet

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Acute, right or obtuse from the sides, Pythagorean triples, and 45-45-90 and 30-60-90 triangles

Grade 10 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

Kira has two sticks, 5 cm and 12 cm long. A third stick is a whole number of centimeters and must close a real triangle. How many lengths make an obtuse triangle?
Luz has two sticks, 8 cm and 15 cm long. A third stick is a whole number of centimeters and must close a real triangle. How many lengths make an obtuse triangle?
Milo has two sticks, 12 cm and 16 cm long. A third stick is a whole number of centimeters and must close a real triangle. How many lengths make an obtuse triangle?
Noah has two sticks, 10 cm and 24 cm long. A third stick is a whole number of centimeters and must close a real triangle. How many lengths make an obtuse triangle?
Not to scale. Tala's quilt patch is a regular hexagon with 8-cm sides. What is its area in square centimeters, in simplest radical form?
Regular hexagon with 10-cm sides. Not to scale. Zee's table top is a regular hexagon with 10-cm sides. What is its area in square centimeters, in simplest radical form?
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Not to scale.
Ari packs a straight rod in a box 2 in by 3 in by 6 in. How long, in inches, is the longest rod that fits from one corner to the opposite corner?
Bo packs a straight rod in a box 4 in by 4 in by 7 in. How long, in inches, is the longest rod that fits from one corner to the opposite corner?
Esme packs a straight rod in a box 3 in by 4 in by 12 in. How long, in inches, is the longest rod that fits from one corner to the opposite corner?
Jun packs a straight rod in a box 9 in by 12 in by 20 in. How long, in inches, is the longest rod that fits from one corner to the opposite corner?

10th grade Acute, right or obtuse from the sides, Pythagorean triples, and 45-45-90 and 30-60-90 triangles worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Special right triangles and the converse. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can tell which set of lengths makes a right triangle, and which third lengths make an obtuse one (the squares and the triangle inequality).
I can find a 30-60-90 or 45-45-90 triangle inside a figure: an equilateral triangle, a rhombus with a 60° angle, a regular hexagon, a square in a circle.
I can use the Pythagorean theorem twice to find the diagonal of a box.

Standard: G-SRT.C.8 (the Pythagorean theorem; special triangles are not named)

Words to know

acute, obtuse: All corners less than 90°; one corner more than 90°.

altitude: The straight line from a corner to the opposite side, meeting it at a right angle.

45-45-90 triangle: Half of a square, cut along its diagonal.

30-60-90 triangle: Half of an equilateral triangle, cut down the middle.

rhombus, regular hexagon: Four equal sides; six equal sides and six equal angles.

simplest radical form: A root with no square factor left inside: 3√2, not √18.

Common mistakes

Your child saw a set that nearly worked and called it right.

Your child trusted a set that has one length changed by 1.

What to say

Ask: do the two shorter squares add to exactly the longest square, or only close?

Ask: is the longest side squared equal to the other two squares added?

Ask: what do the two shorter squares add up to now?

Questions parents ask

What is the most common mistake with acute, right or obtuse from the sides, pythagorean triples, and 45-45-90 and 30-60-90 triangles?

Your child saw a set that nearly worked and called it right.

How can I help my child with acute, right or obtuse from the sides, pythagorean triples, and 45-45-90 and 30-60-90 triangles?

Ask: do the two shorter squares add to exactly the longest square, or only close?

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More geometry

See all Geometry

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