Question

2 the following sentences describe a rectangle.
fill the appropriate words in the blanks.
(1) in a rectangle, since the four are all equal, the two pairs of angles of
the rectangle are equal respectively.
the quadrilateral in which the two pairs of opposite angles are equal respectively, confirms the
property of a , so the rectangle is a parallelogram.
(2) in rectangle abcd on the right,
from ∠abc = ∠dcb = 90°
and bc is shared
△abc ≅ △
from this fact, ac = db is proved.
therefore, the length of the of a rectangle is
shown to be equal.

Explanation:

(1)

Step1: Recall rectangle angle properties

A rectangle has four angles, all equal to \(90^\circ\). So the first blank is "angles".

Step2: Identify opposite angles in rectangle

In a rectangle, the two pairs of opposite angles are equal (all \(90^\circ\) for each, so opposite angles are equal). So the second blank is "opposite".

Step3: Recall parallelogram property

A parallelogram is defined as a quadrilateral with two pairs of opposite angles equal. So the third blank is "parallelogram".

(2)

Step1: Analyze triangle congruence in rectangle

In rectangle \(ABCD\), \(AB = DC\) (opposite sides of rectangle), \(\angle ABC=\angle DCB = 90^\circ\), and \(BC\) is common. By SAS (Side - Angle - Side) congruence criterion, \(\triangle ABC\cong\triangle DCB\). So the first blank is "DCB".

Step2: Identify equal segments from congruence

From \(\triangle ABC\cong\triangle DCB\), we get \(AC = DB\). \(AC\) and \(DB\) are the diagonals of the rectangle. So the second blank is "diagonals".

Answer:

(1) angles; opposite; parallelogram
(2) DCB; diagonals