How many parallel sides can a triangle have?
Answer: A) 0
Explanation: A triangle is a three-sided polygon, and by definition, it cannot have parallel sides. A polygon is a closed shape with straight sides, and parallel sides occur only in polygons with four or more sides. Therefore, a triangle cannot have parallel sides. Option A) is the correct answer. Options B), C), and D) are incorrect, as they imply that a triangle can have one, two, or three parallel sides, which is not possible.
Which of the following triangles have the same side lengths?
A) Equilateral triangle and isosceles triangle
B) Scalene triangle and isosceles triangle
C) Isosceles triangle and right triangle
D) Equilateral triangle and scalene triangle
Answer: A) Equilateral triangle and isosceles triangle
Explanation: An equilateral triangle is a triangle in which all three sides are of equal length, while an isosceles triangle is a triangle in which two sides are of equal length. Therefore, an equilateral triangle can be considered a special case of an isosceles triangle, with all three sides being equal. Thus, option A) is the correct answer.
Option B) is incorrect, as a scalene triangle has no sides of equal length, and an isosceles triangle has at least two sides of equal length. Therefore, they cannot have the same side lengths.
Option C) is incorrect, as an isosceles triangle and a right triangle have different side lengths, except in the special case of a 45-45-90 right triangle, which is also an isosceles triangle.
Option D) is incorrect, as an equilateral triangle and a scalene triangle have no sides of equal length, and therefore cannot have the same side lengths.