Quadrilateral Identification: Equal Sides, Non-Right Angles
This question asks to identify a specific type of quadrilateral based on its properties. We need to find a shape that has four equal sides but does not have four right angles (90 degrees).
Analyzing Quadrilateral Properties
- Equal Sides: The quadrilateral must have all four sides of the same length.
- Angles: The interior angles of the quadrilateral cannot all be right angles.
Evaluating the Options
- Rhombus: A rhombus is defined as a quadrilateral with all four sides equal in length. Its angles are not necessarily right angles. This matches the description.
- Trapezium: A trapezium has at least one pair of parallel sides. Side lengths and angles can vary greatly. This does not fit the criteria.
- Rectangle: A rectangle has four right angles and opposite sides equal. Not all sides are necessarily equal, and it specifically has right angles. This does not fit.
- Square: A square has four equal sides AND four right angles. The condition states angles are NOT right angles, so this is excluded.
Conclusion
Based on the definition, a quadrilateral with equal sides and angles that are not right angles is a rhombus.
Important Questions from Quadrilaterals
What is the value of AC 2– BD 2
What is the area of the parallelogram?
ABCD is a cyclic quadrilateral. Diagonals BD and AC intersect each other at E. If ∠BEC = 138° and ∠ECD = 35°, then what is the measure of ∠BAC?
A circle is inscribed in a quadrilateral ABCD, touching sides AB, BC CD and DA at P, Q, R and S, respectively. If AS = 6 cm, BC = 12 cm, and CR = 5 cm, then the length of AB (in cm) is:
Sides AB and DC of a cyclic quadrilateral ABCD are produced to meet at E and sides AD and BC are produced to meet at F. If ∠ADC = 78° and ∠BEC = 52°, then the measure of ∠AFB is:
