Question

question 7 of 14 submit test geometry module... statements reasons 1. \\( \overline { a b } \cong \overline { a d } ; \overline { b c } \cong \overline { d c } \\) 1. given 2. \\( \overline { a c } \cong \overline { a c } \\) 2. reflexive property of congruence 3. \\( \triangle a b c \cong \triangle a d c \\) 3. 4. \\( \angle a b c \cong \angle a d c \\) 4. which reason justifies the given statement in step 3? sas postulate asa postulate aas theorem sss postulate which reason justifies the given statement in step 4?

Explanation:

Step1: Determine the reason for Step 3

We have \( \overline{AB}\cong\overline{AD}\), \( \overline{BC}\cong\overline{DC}\), and \( \overline{AC}\cong\overline{AC}\). This means all three sides of \( \triangle ABC\) are congruent to the corresponding sides of \( \triangle ADC\). According to the SSS (Side - Side - Side) Postulate, if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. So, the reason for Step 3 is the SSS Postulate.

Step2: Determine the reason for Step 4

Since \( \triangle ABC\cong\triangle ADC\) (from Step 3), by the CPCTC (Corresponding Parts of Congruent Triangles are Congruent) theorem, \( \angle ABC\cong\angle ADC\).

Answer:

• For Step 3: SSS Postulate
• For Step 4: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)