Question

Anastasia wrote the following proof to show that the diagonals of rectangle abcd are congruent: anastasia's proof: statement 1: rectangle abcd is given statement 2: segment ab ≅ segment dc because opposite sides of a rectangle are congruent statement 3: segment ad ≅ segment ad by the reflexive property of congruence statement 4: statement 5: angles bad and adc are congruent because all right angles are congruent statement 6: triangles bad and cda are congruent by sas statement 7: segment ac ≅ segment db by cpctc which statement below completes anastasia's proof? O angles bad and adc are 90 degrees (perpendicular lines create 90 degree angles) O angles bad and abc are 90 degrees (perpendicular lines create 90 degree angles) O angles bad and adc are both right angles (definition of a rectangle) O angles bad and abc are both right angles (definition of a rectangle)

Answer 1

To complete Anastasia's proof, statement 4 should confirm that angles BAD and ADC are both right angles, according to the definition of a rectangle.

Step-by-step explanation:

Anastasia's proof is aimed at showing that the diagonals of a rectangle are congruent. After establishing that segments AB and DC, as well as segments AD and AD, are congruent and that angles BAD and ADC are right angles, she uses the Side-Angle-Side (SAS) Postulate to prove that triangles BAD and CDA are congruent. From there, she can state that the diagonals, AC and DB, are congruent by the Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

To complete Anastasia's proof, the missing statement 4 should explain why angles BAD and ADC are not only congruent but are actually right angles, which is a defining characteristic of a rectangle. Therefore, statement 4 should be: Angles BAD and ADC are both right angles (definition of a rectangle).

Answer 2

Angles BAD and ADC are both right angles (definition of a rectangle).

Statement 4 is missing in Anastasia's proof, and this is where the crucial information about right angles needs to be inserted.

The definition of a rectangle specifies that all four angles in a rectangle are right angles. This means angles BAD and ADC must be right angles.

The other options are not suitable for the following reasons:

"Angles BAD and ADC are 90 degrees (perpendicular lines create 90 degree angles)" is technically correct, but it's not the most precise reason based on the definition of a rectangle.

"Angles BAD and ABC are 90 degrees (perpendicular lines create 90 degree angles)" is incorrect because angle ABC is not relevant to the proof, as it doesn't share a side with the triangles being compared.

"Angles BAD and ABC are both right angles (definition of a rectangle)" is also incorrect because angle ABC is not relevant to the proof.

By stating that angles BAD and ADC are both right angles, based on the definition of a rectangle, Anastasia can then proceed to use the SAS (Side-Angle-Side) congruence criterion to prove that triangles BAD and CDA are congruent, and subsequently conclude that the diagonals AC and BD are congruent.