SOLUTION: Are the following statements true or false, please help! 1.A scalene triangle is never isosceles. 2. An isosceles triangle can be equilateral 3. A scalene triangle is neve

Question 77948: Are the following statements true or false, please help!
1.A scalene triangle is never isosceles.
2. An isosceles triangle can be equilateral
3. A scalene triangle is never right
4. All equilateral triangles are acute
Answer by mszlmb(115) (Show Source): You can put this solution on YOUR website!
1. TRUE

Because a scalene triangle's three sides are all different, no scalene triangle can also be isosceles, meaning that two of it's sides are equal.

2. TRUE

An isosceles triangle has two sides which are equal, or congruent--That's what congruent means in this context, equal. An equilateral triangle has three sides which are equal. Just because an isosceles must have two congruent sides does not mean it can't have three. In fact, every equilateral triangle is also isosceles. Note that not every isosceles triangle is equilateral, as they could have only two sides congruent. We come to the conclusion that an isosceles triangle can be equilateral.

3. FALSE

Scalene simply means that a triangle's sides, and therefore its angles (or vice versa) are not equal. The question is, can we have three different angles (all triangles have three angles and three sides) one of which is 90^o? Yes! Take for example a 30^o-60^o-90^o triangle, or a 50^o-40^o-90^o triangle! In fact, the only triangle with a right (90^o) angle which is not scalene is the 45^o-45^o-90^o triangle, which has two equal angles, and, therefore, two equal sides. Thus a scalene triangle can be right.

4. TRUE

There is only one type of equilateral triangle, the 60^o-60^o-60^o triangle. Because all of the sides must be equal, so must the angles; and vice versa. In such a triangle, only the size varies. The angles are the same. Since for any equilateral triangle, the angles must all be 60^o, all equilateral triangles are acute (they have no angles of a larger degree than 90).
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