Question

consider the following conditional. if all four sides of a quadrilateral are of equal length, then its diagonals intersect at right angles. which of the following figures can be used with the conditional to apply the law of detachment to draw the conclusion that its diagonals intersect at right angles? select each figure that can be used as described above.

Explanation:

Step1: Recall the property

The condition is that if all four - sides of a quadrilateral are of equal length, then its diagonals intersect at right - angles. We need to find figures with all four sides equal.

Step2: Analyze each figure

• Figure A: It is a rhombus. A rhombus has all four sides equal.
• Figure B: It is a parallelogram with adjacent sides equal, but not all four sides are necessarily equal.
• Figure C: It is a rectangle. A rectangle has opposite sides equal, not all four sides equal.
• Figure D: It is a square. A square has all four sides equal.
• Figure E: It is a non - regular quadrilateral, not all four sides are equal.

Answer:

A. Figure A, D. Figure D