Classify the following as true or false. If false, tell why.
_______ (a) A parallelogram has four acute angles.
_______ (b) A line segment contains an infinite number of points.
_______ (c) The union of two rays is always a line.
_______ (d) Every equilateral triangle is a scalene triangle
(a) False. A parallelogram has two pairs of opposite angles, and each pair includes one acute angle and one obtuse angle.
(b) False. A line segment has two endpoints and only contains a finite number of points between those endpoints.
(c) False. The union of two rays can result in different scenarios. If the rays are non-collinear and divergent, their union is not a line. However, if the rays are collinear and share an endpoint, their union will form a line.
(d) False. An equilateral triangle is a triangle with three equal sides and three equal angles, each measuring 60 degrees. A scalene triangle, on the other hand, is a triangle with no equal sides. Therefore, every equilateral triangle is not a scalene triangle.
(a) False: A parallelogram has opposite angles that are congruent, meaning that they have the same measure. Therefore, a parallelogram can have four right angles (also known as 90 degrees angles) or four obtuse angles (greater than 90 degrees), but it cannot have four acute angles (less than 90 degrees).
(b) False: A line segment is a finite portion of a line that connects two points. Therefore, a line segment contains a limited number of points, not an infinite number of points. An example of a line containing an infinite number of points would be a line that extends infinitely in both directions.
(c) False: The union of two rays is not always a line. A ray is a portion of a line that has one endpoint and extends infinitely in one direction. When two rays are joined, they form an angle, not a line.
(d) True: Every equilateral triangle is also a scalene triangle. A scalene triangle is a triangle that has three sides of different lengths. Since all three sides of an equilateral triangle are equal in length, an equilateral triangle can be classified as a scalene triangle.