question
given: $\overline{ad} \cong \overline{db}$ and $\angle cad \cong \angle cbd$.
prove: $\angle cab \cong \angle cba$.
note: quadrilateral properties are not permitted in this proof.
step 1
statement: $\overline{ad} \cong \overline{db}$, $\angle cad \cong \angle cbd$
reason: given

Question

Accepted Answer

# Explanation:
## Step1: Identify isosceles triangle property
Since $\overline{AD} \cong \overline{DB}$, $	riangle ADB$ is isosceles, so $\angle DAB \cong \angle DBA$.
## Step2: Add congruent angle pairs
$\angle CAD + \angle DAB \cong \angle CBD + \angle DBA$
## Step3: Substitute angle sums
$\angle CAB = \angle CAD + \angle DAB$, $\angle CBA = \angle CBD + \angle DBA$, so $\angle CAB \cong \angle CBA$.

# Answer:
$\boldsymbol{\angle CAB \cong \angle CBA}$ is proven as shown above.

Filled two-column proof structure:
| Step | Statement | Reason |
|------|-----------|--------|
| 1 | $\overline{AD} \cong \overline{DB}$, $\angle CAD \cong \angle CBD$ | Given |
| 2 | $\angle DAB \cong \angle DBA$ | Base angles of isosceles $	riangle ADB$ |
| 3 | $\angle CAD + \angle DAB \cong \angle CBD + \angle DBA$ | Addition of congruent angles |
| 4 | $\angle CAB \cong \angle CBA$ | Angle addition postulate (substitution) |

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QUESTION IMAGE

Question

Explanation:

Step1: Identify isosceles triangle property

Step2: Add congruent angle pairs

Step3: Substitute angle sums

Answer:

Step	Statement	Reason
2	$\angle DAB \cong \angle DBA$	Base angles of isosceles $\triangle ADB$
3	$\angle CAD + \angle DAB \cong \angle CBD + \angle DBA$	Addition of congruent angles
4	$\angle CAB \cong \angle CBA$	Angle addition postulate (substitution)