Mathematics Grade 5 15 min

Classify triangles

Classify triangles

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Introduction & Learning Objectives

Learning Objectives Identify a triangle as a polygon with three sides and three angles. Classify triangles by the lengths of their sides as equilateral, isosceles, or scalene. Classify triangles by the measure of their angles as acute, right, or obtuse. Use markings on a triangle (tick marks and right angle symbols) to determine its classification. Understand that a triangle can be classified by both its sides and its angles (e.g., a right isosceles triangle). Apply the rule that the sum of the angles in any triangle is 180° to find a missing angle. Have you ever noticed the shape of a pizza slice or a traffic yield sign? 🍕 You're looking at triangles, and they have special names! In this lesson, you will become a triangle detective! You will learn how to sort, or &#0...
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Key Concepts & Vocabulary

TermDefinitionExample TriangleA polygon with three sides, three vertices (corners), and three angles.A slice of a pie, a yield sign, or a pyramid's face. Acute TriangleA triangle where all three angles are acute (less than 90°).A triangle with angles of 60°, 70°, and 50°. Right TriangleA triangle that has exactly one right angle (exactly 90°).A triangle with angles of 90°, 45°, and 45°. The corner of a square cut in half. Obtuse TriangleA triangle that has exactly one obtuse angle (greater than 90°).A triangle with angles of 110°, 40°, and 30°. Equilateral TriangleA triangle where all three sides are equal in length. All angles are also equal (60°).A triangle with side lengths of 5 cm, 5 cm, and 5 cm. Isosceles TriangleA triangle where at least two sides are equal in length.A triangl...
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Core Formulas

Classification by Sides Equilateral (3 equal sides), Isosceles (2 equal sides), Scalene (0 equal sides) Look at the lengths of the three sides of a triangle. Compare them to see if any are the same length. Tick marks on sides indicate they are equal. Classification by Angles Acute (all 3 angles < 90°), Right (one angle = 90°), Obtuse (one angle > 90°) Look at the measure of the three angles. The type of the largest angle usually determines the classification. A small square in a corner indicates a right angle. Triangle Angle Sum Rule Angle 1 + Angle 2 + Angle 3 = 180° The three interior angles of any triangle always add up to 180 degrees. You can use this rule to find a missing angle if you know the other two.

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Sample Practice Questions

Challenging
Is it possible for a triangle to be both equilateral and isosceles? Why or why not?
A.No, because equilateral means 3 equal sides and isosceles means 2 equal sides.
B.No, because equilateral triangles are always acute.
C.Yes, because an isosceles triangle can sometimes have 3 equal sides.
D.Yes, because the definition of isosceles is 'at least two' equal sides, and an equilateral triangle has three.
Challenging
An isosceles triangle has one angle measuring 50°. Which of the following could be the measures of the other two angles?
A.60° and 70°
B.50° and 80°
C.50° and 50°
D.80° and 80°
Challenging
A student draws a shape and claims it is a triangle with two right angles. Why is this geometrically impossible?
A.triangle can only have acute angles.
B.right triangle must be scalene.
C.Two 90° angles add up to 180°, leaving 0° for the third angle, so the shape cannot close.
D.The two sides forming a right angle can never be equal.

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