Question

in rectangle abcd, describe the relationship between the two objects using the dropdown menu. (options can be used more than once) i. ∠aeb & ∠edc select an answer ii. ∠ace & ∠ecd select an answer iii. ab & bd select an answer iv. ∠aec & ∠ced select an answer v. ae & ed select a vi. ac & db select

Explanation:

Step1: Recall properties of rectangle

In a rectangle, diagonals are equal and bisect each other. Also, vertical angles are congruent.

Step2: Analyze each pair

• i. \(\angle AEB\) and \(\angle EDC\)

\(\angle AEB\) is a vertical angle formed by the intersection of diagonals \(AC\) and \(BD\). \(\angle EDC\) is an angle in the rectangle. There is no significant relationship between them.

• ii. \(\angle ACE\) and \(\angle ECD\)

There is no given information (like diagonal bisecting an angle) to suggest a special relationship. No significant relationship exists.

• iii. \(AB\) and \(BD\)

\(AB\) is a side of the rectangle and \(BD\) is a diagonal. No significant relationship exists.

• iv. \(\angle AEC\) and \(\angle CED\)

These two angles form a linear - pair. So, \(\angle AEC+\angle CED = 180^{\circ}\). They are supplementary.

• v. \(AE\) and \(ED\)

Since diagonals of a rectangle bisect each other, \(AE = ED\). They are congruent.

• vi. \(AC\) and \(DB\)

Diagonals of a rectangle are equal. So, \(AC = DB\). They are congruent.

Answer:

i. No Significant Relationship Exists
ii. No Significant Relationship Exists
iii. No Significant Relationship Exists
iv. Supplementary
v. Congruent
vi. Congruent