Question

question
given: abcd is a parallelogram and \\(\overline{ac} \cong \overline{bd}\\).
prove: \\(\angle abc\\) is a right angle.
step 1
statement: abcd is a parallelogram; \\(\overline{ac} \cong \overline{bd}\\)
reason: given
type of statement
image of a rectangle abcd with diagonals ac and bd intersecting at e

Explanation:

Step1: Use the property of parallelogram with equal diagonals

A parallelogram with equal diagonals is a rectangle.
Since \(ABCD\) is a parallelogram and \(AC\cong BD\), by the property of parallelograms (if the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle).

Step2: Use the property of a rectangle

In a rectangle, all angles are right angles.
Since \(ABCD\) is a rectangle (from Step 1), \(\angle ABC = 90^{\circ}\) (by the definition of a rectangle, which has four right angles).

Answer:

\(\angle ABC\) is a right angle.