Question

given that abcd is a prallelogram with diagonal ac biscet angles bcd, prove that abcd must be a rhomubus

Answer 1

To prove that ABCD is a rhombus, we need to show that all four sides are congruent. Using the properties of parallelograms and the definition of bisected angles, we can prove that ABCD is a rhombus.

Step-by-step explanation:

To prove that ABCD is a rhombus, we need to show that all four sides are congruent. Since ABCD is a parallelogram and has diagonals that bisect the angles, we can use the properties of parallelograms and the definition of bisected angles to prove that it is a rhombus.

First, we know that opposite angles of a parallelogram are congruent, so angle ACD is congruent to angle CAB (opposite angles of the parallelogram ABCD).

Next, we know that opposite angles of the parallelogram ABCD are bisected by the diagonals. Therefore, angle BCD is congruent to angle BAC (bisected angles of the parallelogram ABCD).

Using the properties of angles, we can conclude that angle ABC is congruent to angle CAB (transitive property of congruence).

Since angle ABC is congruent to angle CAB and opposite angles of a parallelogram are congruent, we can conclude that ABCD is a rhombus, as all four angles are congruent.