Problem 21
This triangle is equilateral since it has three equal sides. The tickmarks tell us each side is the same length. The triangle is also acute since each angle is less than 90.
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Problem 22
There aren't any tickmarks here, so the sides aren't the same length. All three sides are different which makes this triangle scalene. The triangle is also acute since each angle is less than 90.
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Problem 23
We have an isosceles obtuse triangle here.
Isosceles because of the two congruent sides (shown by the tickmarks).
Obtuse due to the angle larger than 90 degrees.
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Problem 24
This is an isosceles right triangle
The square marker indicates a right angle aka 90 degree angle.
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Problem 25
This is a right triangle that is scalene since there aren't any tickmarks, so each side is of a different length.
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Problem 26
This is an isosceles right triangle
See problem 24.
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Problem 27
This is an isosceles triangle that is also acute
The two similar tickmarks tell us the triangle is isosceles. Each angle is less than 90 so that's why the triangle is acute. We have similar situations as problems 21 and 22.
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To recap we have these three terms to tell us about the side lengths
- equilateral = all sides the same length
- isosceles = exactly two sides are the same length (third side is something different)
- scalene = all three sides are different lengths
And we have these terms to describe the angles
- acute = all 3 angles are smaller than 90 degrees
- right = exactly one angle is 90 degrees, shown by a square marker
- obtuse = exactly one angle is over 90 degrees (the other two angles are acute)
We can then mix and match some of the terms to form combos like "isosceles right triangle" or "obtuse scalene".
Some terms can't be mixed. For example, we can't have an equilateral right triangle. This is because a right triangle has the hypotenuse always as the largest side, but equilateral triangles have all sides the same length. There's a contradiction if we combined those terms.
Another impossible combo is to have "equilateral" and "obtuse" put together. The reasoning is similar as mentioned in the previous paragraph.
Check out the diagram below to see a table of all possibilities.