Question

Please do it in such a way where you draw a line from A to C to use in your explanation. Also please draw the diagram so I can visualize.

Answer 1

We have to prove that triangles ABC and ADC are congruents.

We can draw a driagram of the triangles as:

As AB and AD are radius of the same circle, we have:

$AB\cong AD$

The same can be said for CB and CD, so:

$CD\cong CD$

Then, we have a shared side between the two triangle. Then, given the reflexive property we have:

$AC\cong AC$

Then, as we have 3 pair of congruent sides, by the SSS postulate, we can conclude that the triangles ABC and ADC are congruent. Then, all three pair of angles are also congruent.

NOTE:

If we just want to prove that the angles Then, we four right triangles (or a rhombus). Then, each angle of the erhombus is bisected.

The left angle at vertex D is complementary to the lower angle at A. The left angle at vertex B is complementary to the upper angle at A. As both angles at A are equal, The left angle at D and the left angle at B are complementary to the same angle.

Then, they have the same measure.

The same analysis can be done for the right angles.

Then, as both halves of the angles are equal, then the total angle