What do these shapes have in common? Answer A) Both are isosceles triangles; B) both are equilateral triangles; C) both are obtuse triangles; D) both are acute triangles; or E) both are right triangles.
So what I’m going to do in this question is go through each answer in turn and see whether it’s true or false. Well answer A says both are isosceles triangles. And an isosceles triangle is a triangle that has two sides the same length, and also two angles, the base angles, are also the same. Well if we take a look at our diagram, there are some lines here that help us. These lines, so the two lines on the first triangle and single lines in the second triangle, tell us that these sides are equal. So therefore, we have a pair of equal sides in each of our triangles. So therefore, we can say that yes both of them are isosceles triangles. So this is true.
So now let’s move on to answer B: both are equilateral triangles. Well if you think about equilateral triangles, equilateral triangles have three equal sides, and all three angles are the same. And it can be notated using small lines saying that each side is the same, and I’ve shown that on the diagram I’ve drawn here. Well as we’ve already discussed, our triangles only have two sides the same. So therefore, they are not both equilateral triangles. So now we can move on to answer C: both are obtuse triangles. Well an obtuse triangle is a triangle that has one angle that is greater than 90 degrees and two angles that are less than 90 degrees. Well if we take a look at our second triangle, we can see that has an angle that is 90 degrees. So therefore it cannot be an obtuse triangle. So therefore we can’t say that both are obtuse triangles.
Well if we take a look at answer D, it says both are acute triangles. Well an acute triangle is a triangle whose angles are all less than 90 degrees. So therefore, we can say that ours cannot be both acute triangles because, as we already pointed out, the second triangle has an angle which is 90 degrees. And the first triangle may be an acute triangle, but as they’re not drawn accurately, we couldn’t say for sure. But we can definitely say that both are not acute triangles because the second triangle contains an angle which is 90 degrees. Now finally, we move on to answer E, which says that both are right triangles. Well if we take a look at the second triangle, this is a right triangle because one of the angles is a right angle so it’s 90 degrees. However, we haven’t got any right angles in the first triangle cause we haven’t gotten those marked on. So therefore, we can say that they cannot be both right triangles.
So therefore in answer to the question what do these shapes have in common, the answer is answer A: both are isosceles triangles. And that’s because they have two equal sides and, therefore, two corresponding base angles which will be also equal.