Question

Consider parallelogram ABCD. Choose all of the statements which must be true

Answer 1

The answers are 1, 2, and 4. Look at the parallelogram's angles to be sure.

Answer 2

`AE=EC`

`\angle ADB \cong \angle CBD`

`m\angle ADC + m\angle DCB = 180\°`

Explanation:

In the given parallelogram, we know that

`AD \parallel BC\\AB \parallel DC`

From this parallels and having segment
`DB` as a transversal, we have

`\angle ADB \cong \angle CBD` by alternate interior angles.

Then, we have

`AE=EC` by givens.

Finally, we have

`m\angle ADC + m\angle DCB = 180\°` , by consecutive interior angles, which are supplementary by definition.

Therefore, the right answers are

`AE=EC`

`\angle ADB \cong \angle CBD`

`m\angle ADC + m\angle DCB = 180\°`