Question

1. as shown in the figure below, in rt△abc, m∠acb = 90°, and cd⊥ab at point d, ce∥ab, eb∥cd, and draw de such that it intersects bc at point o. prove that de = bc. 6. which of the following properties are shown in rhombi but not necessarily rectangles? a. diagonals are equal b. diagonals bisect each other c. diagonals are perpendicular d. adjacent sides are perpendicular

Explanation:

5.

Step1: Prove BCDE is a parallelogram

Since $CE\parallel AB$ and $EB\parallel CD$, according to the definition of a parallelogram (a quadrilateral with two - pairs of parallel sides), quadrilateral $BCDE$ is a parallelogram.

Step2: Use property of parallelogram

In a parallelogram, opposite sides are equal. In parallelogram $BCDE$, $DE$ and $BC$ are opposite sides. So $DE = BC$.

Recall the properties of rhombi and rectangles. Diagonals of a rhombus are perpendicular bisectors of each other, while diagonals of a rectangle are equal and bisect each other. Adjacent sides of a rectangle are perpendicular. Diagonals bisect each other in both rhombi and rectangles.

Answer:

Proved that $DE = BC$ as $BCDE$ is a parallelogram.

6.