Question

Given: ABCD with diagonal line BD Prove: triangle ABD is congruent triangle CDB

Answer 1

Answer:

It is given that:

ABCD is a parallelogram with diagonal line BD.

To prove that: $\triangle ABD \cong \triangle CDB$

Properties of parallelogram:

• Opposite sides are parallel

• Opposite sides are congruent  

• Opposite angles are congruent

• Diagonal bisects each other.

In $\triangle ABD$ and $\triangle CDB$

By definition of parallelogram;

$\overline{AD} || \overline{BC}$

$\overline{AB} || \overline{CD}$

Alternative interior angle theorem says that if the two parallel lines are cut by transversal, then the pairs of alternative interior angles are congruent.

by alternative interior angle theorem;

$\angle ADB \cong \angle CBD$

$\angle ABD \cong \angle CDB$

By reflexive property:

$\overline{DB} || \overline{DB}$  

ASA(Angles sides Angle) postulates states that if two angles and the included side of one triangle to corresponding parts of the another triangle, then the triangles are congruent.

⇒$\triangle ABD \cong \triangle CDB$  

Answer 2

3. definition of parallelogram
4. alternate interior angles theroem
5. reflexive property of congruence
6. ASA