Which statement about the relationship between different types of triangles is true?
A) An equilateral triangle is never an obtuse triangle.
B) An equilateral triangle is never an isosceles triangle.
C) A right triangle is always an isosceles triangle.
D)An obtuse triangle is always an acute triangle.
ok
To determine which statement about the relationship between different types of triangles is true, we need to understand the characteristics of each type of triangle.
1. Equilateral triangle: All three sides and angles are equal.
2. Obtuse triangle: It has one angle greater than 90 degrees.
3. Isosceles triangle: It has two sides of equal length.
4. Right triangle: It has one angle equal to 90 degrees.
5. Acute triangle: All three angles are less than 90 degrees.
Now, let's analyze each statement:
A) An equilateral triangle is never an obtuse triangle:
To check the validity of this statement, we need to consider the definition of an equilateral triangle (all sides and angles are equal) and an obtuse triangle (has one angle greater than 90 degrees). Since all angles in an equilateral triangle measure 60 degrees, it is impossible for it to have an angle greater than 90 degrees. So, statement A is true.
B) An equilateral triangle is never an isosceles triangle:
An isosceles triangle has two sides of equal length. Since an equilateral triangle has all three sides equal, it automatically fulfills the condition of an isosceles triangle. Therefore, statement B is false.
C) A right triangle is always an isosceles triangle:
A right triangle has one angle measuring 90 degrees. While it is true that a right triangle can be an isosceles triangle if its other two angles are acute and congruent (45 degrees), it is not always the case. For example, a right triangle with angles measuring 30 degrees, 60 degrees, and 90 degrees is not an isosceles triangle. Thus, statement C is false.
D) An obtuse triangle is always an acute triangle:
An obtuse triangle has one angle greater than 90 degrees, while an acute triangle has all angles less than 90 degrees. Since the two types of triangles have opposite characteristics, this statement is false.
In conclusion, the only true statement is:
A) An equilateral triangle is never an obtuse triangle.
A) how about sides of 5,5, and 8 ?
B) doesn't an equilateral have 3 equal sides, so obviously 2 equal sides?
C) ooh, ooh, I am thinking of the 3,4, 5 right-angled triangle.
D) the statement itself is a contradiction.