In a proof that the diagonals of rectangle ABCD
are congruent, which statement comes just after the statements that AD¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯
, AB¯¯¯¯¯¯¯¯≅AB¯¯¯¯¯¯¯¯
, and ∠DAB≅∠CBA
?
The statement that comes just after the given statements is "Therefore, the diagonals of rectangle ABCD are congruent."
△DAB≅△AOB
triangle upper A upper D upper B congruent to triangle upper C upper B upper D
△DAB≅△DOC
triangle upper A upper O upper D congruent to triangle upper C upper O upper B
△DAB≅△DAO
triangle upper A upper C upper D congruent to triangle upper C upper A upper B
△DAB≅△CBA
triangle upper A upper O upper B congruent to triangle upper D upper O upper C
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these are the answer choices.
The correct answer choice would be "△DAB≅△CBA, triangle AOB is congruent to triangle DOC, and triangle ADO is congruent to triangle COB."
To determine which statement comes just after the given statements in the proof that the diagonals of rectangle ABCD are congruent, we need to understand the properties of a rectangle.
In a rectangle, opposite sides are congruent and all angles are right angles. Let's analyze the given statements and use these properties to determine the next statement in the proof:
1. AD¯¯¯¯¯¯¯¯ ≅ BC¯¯¯¯¯¯¯¯ (Given)
This states that the side AD is congruent to side BC. It implies that the opposite sides of the rectangle are congruent.
2. AB¯¯¯¯¯¯¯¯ ≅ AB¯¯¯¯¯¯¯¯ (Given)
This states that side AB is congruent to itself, which is always true for any line segment.
3. ∠DAB ≅ ∠CBA (Given)
This states that angle DAB is congruent to angle CBA. It implies that all angles in the rectangle are right angles.
Based on these statements, we can conclude that we have a rectangle with congruent opposite sides and right angles at all vertices.
The next statement in the proof would typically be:
4. ABCD is a rectangle (Conclusion)
This statement formally concludes that the figure ABCD satisfies all the properties of a rectangle, based on the previous statements.