Question

question 1 of 5. select the correct answer from each drop - down menu. amma completes the construction below. is quadrilateral bcde a square? quadrilateral bcde is a square. segment bd is < > measure of each central angle is. so, arcs bc, of quadrilateral bcde are all congruent. the angles of quadrilateral bcde all cut of an arc that mea congruent. half the length of perpendicular to double the length of parallel to diameter ce. therefore, the e that same measure. so, the sides is of quadrilateral bcde are all

Explanation:

Step1: Recall properties of a square

In a square, the central - angles are equal. The sum of central angles around a point is 360°. Since a square has 4 equal central angles, each central angle $\theta=\frac{360^{\circ}}{4} = 90^{\circ}$.

Step2: Recall relationship between arc - length and central - angle

If the central angles are equal, the arcs they subtend are congruent. In a square inscribed in a circle, the sides of the square are chords and the arcs between the endpoints of the chords are congruent because the central angles are congruent.

Step3: Recall properties of diagonals of a square

The diagonals of a square are equal in length. For a square BCDE inscribed in a circle with center A, segment BD and segment CE are diagonals of the square. They are equal in length. Also, the sides of a square are equal. Since the angles of the square cut off congruent arcs, the sides of the square are chords of equal - length arcs.

Answer:

Each central angle is 90°. So, arcs BC, CD, DE, EB are congruent. The sides of quadrilateral BCDE are all congruent. Segment BD is equal in length to segment CE.