b Is this a right triangle? Can you investigate that with a certain theorem?
C
c What's true for the base angles of an isosceles triangle?
A
a The sides do not create a triangle.
B
b This is not a right triangle.
C
c The triangle cannot be isosceles.
Practice makes perfect
a According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle is greater than the length of the third side. Let's try this for the triangle's sides.
3 + 9? >5& ⇔ 12> 5
5 + 9? >3& ⇔ 14> 3
3 + 5? >9& ⇔ 8 ≯ 9
Therefore, a triangle with the given measurements does not exist.
b Let's test the triangle inequality theorem to make sure this is not the error.
5 + 14&? >12 &&⇔ 19> 12
14 + 12&? >5 &&⇔ 26> 5
12 + 5&? >14 &&⇔ 17 > 14We can definitely create a triangle with the given measurements. However, are these side lengths going to create a right triangle? If they do, the Pythagorean Theorem has to hold true.
Since the Pythagorean Theorem does not hold true, a triangle with these measurements is not a right triangle.
c From the diagram, we see that this should be an isosceles triangle as it has two congruent sides of 7 inches. This requires it's base angles to be congruent as well. We know that one of them is 65^(∘). To find the other, we have to subtract the two known angles from 180^(∘).
180^(∘)-55^(∘)-65^(∘)=60^(∘)
As we can see, the last angle is 60^(∘) given the two angles in the diagram. Therefore this cannot be an isosceles triangle.
