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

Answer:

$AE=EC$

$\angle ADB \cong \angle CBD$

$m\angle ADC + m\angle DCB = 180\°$

Step-by-step 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

$AE=EC$

$\angle ADB \cong \angle CBD$

$m\angle ADC + m\angle DCB = 180\°$