Question

hi || jk. complete the proof that △hjk ≅ △jhi.

statement
1
2
3
4
5

reason
given
given
alternate interior angles theorem
reflexive property of congruence

Explanation:

Step1: Analyze the given information

We are given that \( \overline{HI}\parallel\overline{JK}\) and some other congruent segments.

Step2: Use the Alternate Interior Angles Theorem

Since \( \overline{HI}\parallel\overline{JK}\), by the Alternate Interior Angles Theorem, \( \angle HJK\cong\angle IHJ\)

Step3: Use the Reflexive Property

\( \overline{HJ}\cong\overline{HJ}\) by the Reflexive Property of Congruence

Step4: Use the SAS (Side - Angle - Side) Congruence Criterion

We know that \( \overline{HK}\cong\overline{JI}\) (given), \( \angle HJK\cong\angle IHJ\) (from step 2), and \( \overline{HJ}\cong\overline{HJ}\) (from step 3).
By the SAS congruence criterion, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Answer:

\(\triangle HJK\cong\triangle JHI\) by the SAS (Side - Angle - Side) congruence criterion.