Classifying triangles Worksheets - Free Printable

Let's analyze the triangle shown in the image:

Given:

- One angle is 90° (indicated by the right angle symbol).
- Two angles are 45° each.
- Side lengths: one leg is 4.8, the other leg is also 4.8, and the hypotenuse is 6.8.

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Step 1: Check the angles

We know that:
- The sum of angles in a triangle is 180°.
- We have: 90° + 45° + 45° = 180° → ✔

So, this is a right triangle because it has a 90° angle.

Also, since two angles are equal (45°), the sides opposite them must be equal. Indeed, both legs are 4.8, so the triangle has two equal sides.

That means it is an isosceles triangle.

Therefore, this is a right isosceles triangle.

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Step 2: Check side lengths

- Two sides are equal (4.8 and 4.8) → isosceles
- One angle is 90° → right triangle

So, combining both: right isosceles triangle

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Step 3: Evaluate the options

A) right isosceles → ✔ Correct
B) scalene isosceles → ✘ Contradictory (scalene means no equal sides, isosceles means two equal sides)
C) obtuse scalene → ✘ It’s not obtuse (no angle > 90°), and not scalene
D) acute scalene → ✘ Not acute (has a 90° angle), and not scalene

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✔ Final Answer: A) right isosceles