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Geometry reference

Triangle facts reference

Review triangle parts, the 180-degree interior-angle sum, side classifications and angle classifications in one fixed two-page handout with six exact diagrams for Letter or A4 paper.

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Read the two reference pages. Compare the exact diagrams, definitions and combined angle-and-side facts.

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Read triangle facts from exact geometry

The first page names the three sides, three interior angles and 180-degree sum, then compares equilateral, isosceles and scalene triangles with exact side markings.

The second page compares acute, right and obtuse triangles, then shows how angle and side descriptions combine. Both preview pages are the complete fixed reference.

Learning objective

What this activity builds

Connect side markings and angle measures to equilateral, isosceles, scalene, acute, right and obtuse triangle facts.

Worked example

Can an equilateral triangle also be called isosceles?

Yes.

An isosceles triangle has at least two equal sides. An equilateral triangle has three equal sides, so it meets that definition. Classification practice still uses Equilateral as the most specific answer label.

Teaching notes

Make the practice count

  • Read the side and angle facts separately before combining them.
  • Match tick counts to decide which sides have equal length.
  • Use 90 degrees as the boundary between acute, right and obtuse classifications.
  • Keep the inclusive isosceles definition visible when discussing equilateral triangles.

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Math SheetNameDateTriangle factsTriangle foundationsEvery triangle has three straight sides and three interior angles. The interior angles always add to 180°.Equilateral60°60°60°3 equal sides · 60°, 60°, 60°IsoscelesAt least 2 equal sides · equal base anglesScaleneNo equal sides or anglesClassify by side length• Matching tick counts mark equal lengths. Different tick counts in these examples distinguish unequal lengths.Equilateral• Three equal sides and three equal angles. Each angle is 60°.Isosceles• At least two equal sides. The angles opposite those equal sides are equal.Scalene• No equal sides and no equal angles.Inclusive definition• An equilateral triangle is also isosceles because it has at least two equal sides. In classification practice, use Equilateral asthe specific answer label.math-sheet.comPage 1 / 2
Math SheetNameDateTriangle factsClassify by angle sizeLook at the largest interior angle. A triangle is acute, right or obtuse.Acute< 90°All angles < 90°Right90°One angle = 90°Obtuse> 90°One angle > 90°Acute• All three interior angles are less than 90°.Right• Exactly one interior angle is 90°.Obtuse• Exactly one interior angle is greater than 90°.Combine angle and side facts• Acute scalene: all angles are less than 90°; no sides are equal.• Acute isosceles: all angles are less than 90°; at least two sides are equal.• Right scalene: one angle is 90°; no sides are equal.• Right isosceles: two sides are equal; the angles are 90°, 45° and 45°.• Obtuse scalene: one angle is greater than 90°; no sides are equal.• Obtuse isosceles: one angle is greater than 90°; at least two sides are equal.Remember• An equilateral triangle has three 60° angles, so it belongs to the acute and isosceles groups too. Use Equilateral as itsspecific answer label in classification practice.math-sheet.comPage 2 / 2

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