Question

11/14 - triangle congruence schoology assignment
possible points: 0.58
why is ( \triangle abc cong \triangle ghj )?
choose the correct answer below.
o a. since ( \triangle abc cong \triangle def ) by sas and ( \triangle def cong \triangle ghj ) by sss, ( \triangle abc cong \triangle ghj ) by the transitive property of congruence.
o b. since ( \triangle abc cong \triangle def ) by sss and ( \triangle def cong \triangle ghj ) by sas, ( \triangle abc cong \triangle ghj ) by the transitive property of congruence.
o c. since ( overline{ac} cong overline{gj} ) and ( overline{cb} cong overline{jh} ), ( angle c ) must be congruent to ( angle j ). so, ( \triangle abc cong \triangle ghj ) by sas.
o d. since ( overline{ac} cong overline{gj} ) and ( overline{cb} cong overline{jh} ), ( overline{ab} ) must be congruent to ( overline{gh} ). so, ( \triangle abc cong \triangle ghj ) by sss.
o a.
o b.
o c.
o d.

Explanation:

Step1: Analyze triangle \(ABC\) and \(DEF\)

Looking at \(\triangle ABC\) and \(\triangle DEF\), we can see that all three sides of \(\triangle ABC\) are congruent to the corresponding sides of \(\triangle DEF\). So, \(\triangle ABC\cong\triangle DEF\) by SSS (Side - Side - Side) congruence criterion.

Step2: Analyze triangle \(DEF\) and \(GHJ\)

For \(\triangle DEF\) and \(\triangle GHJ\), two sides and the included angle are congruent. So, \(\triangle DEF\cong\triangle GHJ\) by SAS (Side - Angle - Side) congruence criterion.

Step3: Use the Transitive Property of Congruence

Since \(\triangle ABC\cong\triangle DEF\) and \(\triangle DEF\cong\triangle GHJ\), by the Transitive Property of Congruence (if \(a = b\) and \(b = c\), then \(a = c\) for congruent triangles), \(\triangle ABC\cong\triangle GHJ\).

Answer:

B. Since \(\triangle ABC\cong\triangle DEF\) by SSS and \(\triangle DEF\cong\triangle GHJ\) by SAS, \(\triangle ABC\cong\triangle GHJ\) by the Transitive Property of Congruence.