Question

1. what is not true about this shape?

a) it has perpendicular line segments.
b) it has parallel line segments.
c) it has an obtuse angle.
d) it has no acute angles.

Explanation:

Step1: Recall properties of a rectangle

A rectangle has four right - angles (90 degrees). Right - angles are neither acute (less than 90 degrees) nor obtuse (greater than 90 degrees). A rectangle has two pairs of parallel line segments (opposite sides are parallel) and four pairs of perpendicular line segments (adjacent sides are perpendicular).

Step2: Analyze each option

• Option a: Since a rectangle has four right - angles (90 degrees), and right - angles are perpendicular (the product of slopes of two lines forming a right - angle is - 1 in coordinate geometry, and in Euclidean geometry, adjacent sides meet at 90 degrees). So, it has perpendicular line segments. This statement is True.
• Option b: A rectangle has two pairs of parallel line segments (opposite sides are parallel). So, this statement is True.
• Option c: A rectangle has four right - angles (90 degrees). Since \(90\lt180\), a right - angle is not an obtuse angle (\(\text{obtuse angle}>90^{\circ}\) and \(< 180^{\circ}\)). So, this statement is False.
• Option d: Since a rectangle has four right - angles (\(90^{\circ}\)), and \(90>0\) and \(90 < 90\) (acute angle \(<90^{\circ}\)), it has no acute angles. This statement is True.

Answer:

C. It has an obtuse angle.