Question

question 1 - 12
use the diagram to answer the questions and complete the proof.
given: \\( \overline { a b } \cong \overline { a d } ; \overline { b c } \cong \overline { d c } \\)
prove: \\( \angle a b c \cong \angle a d c \\)
which reason justifies the given statement in step 3?
asa postulate
sas postulate
sss postulate
aas theorem
which reason justifies the given statement in step 4?
vertical angles theorem
sas postulate
corresponding parts of congruent triangles are congruent
symmetric property of triangle congruence

Explanation:

Step1: Determine congruence postulate for Step 3

We have \(AB\cong AD\), \(BC\cong DC\), and \(AC\cong AC\) (common side). This is three - sides congruence.

Step2: Determine reason for Step 4

If two triangles are congruent (\(\triangle ABC\cong\triangle ADC\)), then their corresponding parts are congruent.

Answer:

For Step 3: SSS Postulate.
For Step 4: Corresponding parts of congruent triangles are congruent.