Which of the following describes the given shape? a) acute scalene triangle, b) acute isosceles triangle, c) right isosceles triangle, d) obtuse isosceles triangle, or e) a right scalene triangle.
Well it’s an enclosed shape with three straight sides, so it is a triangle; it’s a polygon with three sides And these little markers here and here tell us that those two sides are the same length. And triangles with two sides the same length are called isosceles triangles.
Remember, scalene means that all the different sides of the triangle will be different lengths, so any triangle that says it’s a scalene triangle doesn’t match the diagram that we’ve got here. So that leaves us with three choices. Either it’s an acute isosceles triangle, a right isosceles triangle, or an obtuse isosceles triangle.
Now you should remember that the base angles in an isosceles triangle are equal, and that’s these two angles here. They’re the angles which are the angle where the sides of the same length meet.
Now remember an acute angle is one which is between zero degrees and ninety degrees, and an obtuse angle is between ninety degrees and one hundred and eighty degrees, and a right angle is exactly ninety degrees. Remember the sum of the measures of the interior angles in a triangle is a hundred and eighty degrees.
Now that means that this angle and this angle have each got to be acute. They’ve got to be less than ninety degrees. If they were ninety degrees or more, then we’d have a sum of angles which is greater than hundred and eighty degrees for a triangle. So that wouldn’t work. So when we talk about acute, right, or obtuse, we can’t be talking about these angles here in an isosceles triangle. We must be talking about the other angle. So the question is is it acute, is it right, or is it obtuse.
Well that symbol there means it’s ninety degrees, which makes it a right angle. And this means we’ve got a right isosceles triangle. So our answer is c, right isosceles triangle.