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 Law of Detachment

The Law of Detachment states that if a conditional statement is true and its hypothesis is met, then its conclusion is true. The conditional is: If all four sides of a quadrilateral are of equal length, then its diagonals intersect at right - angles.

Step2: Analyze each figure

We need to find figures where all four sides are of equal length. A rhombus (including squares which are a special type of rhombus) has all four sides equal.

• Figure A is a parallelogram but not all sides are necessarily equal.
• Figure B is a square (a type of rhombus) with all four sides equal.
• Figure C is a rhombus with all four sides equal.
• Figure D is a rectangle, and its adjacent sides are not necessarily equal.
• Figure E is a rhombus with all four sides equal.

Answer:

B. Square, C. Rhombus, E. Rhombus