Question

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what is m∠hji? justify your answer.

a. △def≅△hij by sas. by cpctc, ∠dfe≅∠hji. thus, m∠hji = f.
b. △def≅△hij by sss. by cpctc, m∠def + m∠edf=∠hji. thus, m∠hji = d + e.
c. △def≅△hij by sas. by cpctc, ∠def≅∠hji. thus, m∠hji = e.
d. △def≅△hij by sss. by cpctc, ∠edf≅∠hji. thus, m∠hji = d.

Explanation:

Step1: Identify congruence criterion

From the markings on the triangles, we see two - pairs of congruent sides and the included angles are congruent, so $\triangle DEF\cong\triangle HIJ$ by SAS (Side - Angle - Side) congruence criterion.

Step2: Use CPCTC

CPCTC (Corresponding Parts of Congruent Triangles are Congruent). If $\triangle DEF\cong\triangle HIJ$ by SAS, then the corresponding angles are congruent. The angle corresponding to $\angle HJI$ in $\triangle DEF$ is $\angle DFE$. So, $\angle DFE\cong\angle HJI$ and $m\angle HJI = f$.

Answer:

A. $\triangle DEF\cong\triangle HIJ$ by SAS. By CPCTC, $\angle DFE\cong\angle HJI$. Thus, $m\angle HJI = f$.