Question 5 - Figure it out - Page 94 - Chapter 4 Class 8 - Quadrilaterals (Ganita Prakash)

Transcript

Question 5 We saw that one of the properties of a rectangle is that its opposite sides are parallel. Can this be chosen as a definition of a rectangle? In other words, is every quadrilateral that has opposite sides parallel and equal, a rectangle?No. Let’s take an Example Properties Check: Opposite Sides Parallel? ✓ Yes to Opposite Sides Equal? Yes Is it a Rectangle? × NO Slant the Shape (Shear) Drag the slider. Notice that even though the sides stay parallel and equal length, the corners are not . Reset to RectangleReasoning: A quadrilateral with opposite sides parallel and equal is the definition of a Parallelogram. While all rectangles are parallelograms, not all parallelograms are rectangles. For example, a "slanted" parallelogram (like a rhombus or a general rhomboid) has opposite sides that are parallel and equal, but its corner angles are not 90° To define a rectangle, you must add one more condition: either "one angle is 90° " or "the diagonals are equal in length". Reasoning: A quadrilateral with opposite sides parallel and equal is the definition of a Parallelogram. While all rectangles are parallelograms, not all parallelograms are rectangles. For example, a "slanted" parallelogram (like a rhombus or a general rhomboid) has opposite sides that are parallel and equal, but its corner angles are not 90° To define a rectangle, you must add one more condition: either "one angle is 90° " or "the diagonals are equal in length".