Question

7 from unit 1, lesson 22 this design began from the construction of a regular hexagon. is quadrilateral jklo congruent to the other two quadrilaterals? explain how you know.

Explanation:

Step1: Properties of a regular hexagon

A regular hexagon has all sides equal and all internal angles equal. The construction of the hexagon implies that the sides of the quadrilaterals (which are formed within the hexagon) are related to the side - length of the hexagon.

Step2: Congruence of quadrilaterals

Since the design is based on the construction of a regular hexagon, the lengths of the corresponding sides of quadrilateral \(JKLO\), \(ABHG\), and \(BCHI\) are equal. Also, the angles between the corresponding sides of these quadrilaterals are equal. By the Side - Angle - Side (SAS) congruence criterion (for parallelograms, as these quadrilaterals are parallelograms within the regular hexagon structure, all corresponding sides and angles are equal).

Answer:

Yes, quadrilateral \(JKLO\) is congruent to the other two quadrilaterals. Because in a regular hexagon - based construction, all corresponding sides and angles of the parallelogram - shaped quadrilaterals (\(JKLO\), \(ABHG\), \(BCHI\)) are equal.