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Classifying Triangles Notes

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Classifying Triangles Notes

Use the notes and clues to investigate triangles. A triangle can be classified by its sides, its angles, or both.

Quick notes

CLASSIFY BY SIDES • Equilateral: three equal sides; three 60° angles. • Isosceles: exactly two equal sides; the angles opposite those sides are equal. • Scalene: three different side lengths. CLASSIFY BY ANGLES • Acute: all three angles are less than 90°. • Right: one angle is exactly 90°. • Obtuse: one angle is greater than 90°. Every triangle’s angles total 180°. The two shorter sides together must be longer than the longest side. A triangle can have one side classification and one angle classification.

Orchard support challenge

Sienna and Layla are checking triangular braces for fruit-orchard signs. Read each set of measurements carefully. Angles in each triangle are listed in vertex order.

1.Brace A has side lengths 5 cm, 5 cm and 8 cm. Classify it by its sides and explain the clue you used.

2.Brace B has angles 90°, 35° and 55°. What is its angle classification?

Acute
Right
Obtuse

3.Brace C has side lengths 6 cm, 6 cm and 6 cm. Its angles are 60°, 60° and 60°. Give its classification by sides and by angles.

4.Evie measures a triangle’s angles as 48°, 72° and 60°. Do these measurements make a triangle? Show the total and explain.

5.A triangular orchard sign has angles of 42°, 98° and x°. Find x, then classify the triangle by its angles.

6.A triangle with side lengths 4 cm, 7 cm and 12 cm can be built. Decide whether this is true or false and use the side rule to justify your answer.

TrueFalse

7.Sienna has sticks of 5 cm, 7 cm and 9 cm. Can they form a triangle? Check the side rule and classify the possible triangle by its sides.

8.Match each angle set with its angle classification.

35°, 65°, 80°
90°, 25°, 65°
110°, 30°, 40°

Right
Acute
Obtuse

9.In an isosceles triangle, the two equal sides are 7 cm each. The angle between those equal sides is 40°. What are the other two angles?

10.Draw a scalene, acute triangle. Label its three side lengths with different numbers and write three angle measures that total 180° and are all less than 90°.