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. learning target + i can write a proof that segments of the same length are congruent.

Explanation:

Since the design began from the construction of a regular hexagon, all the sides of the hexagon are equal and all the internal angles are equal. The quadrilaterals are formed in a symmetrical way within the regular hexagon. In a regular hexagon, due to its rotational and reflectional symmetry, the shapes (quadrilaterals in this case) formed in congruent - looking positions (like \(JKLO\) and the other two) will have all corresponding sides and angles equal. For example, the sides of the quadrilaterals are made up of segments that are either sides of the hexagon or segments created by the equal - spaced construction within the hexagon. Also, the angles of the quadrilaterals are derived from the angles of the regular hexagon (\(120^{\circ}\) and \(60^{\circ}\) related angles when considering the parallelogram - like shapes of the quadrilaterals).

Answer:

Yes, quadrilateral \(JKLO\) is congruent to the other two quadrilaterals. Because the design is based on a regular hexagon, which has rotational and reflectional symmetry. The sides and angles of the quadrilaterals are determined by the properties of the regular hexagon (equal side lengths and specific angle measures). All corresponding sides and angles of \(JKLO\) and the other two quadrilaterals are equal, so they are congruent.