Question

hi || jk. complete the proof that △hij ≅ △jkh.

statement
1 jk ≅ hi
2 hi || jk
3 ∠hjk ≅ ∠ihj
4 hj ≅ hj
5 △hij ≅ △jkh

reason
given
given
alternate interior angles theorem
reflexive property of congruence
cpctc
definition of congruence
sas
sss

Explanation:

Step1: Analyze the given information

We are given that \( \overline{JK}\cong\overline{HI}\), \( \overline{HI}\parallel\overline{JK}\), \( \angle HJK\cong\angle IHJ\) (by Alternate Interior Angles Theorem as \( \overline{HI}\parallel\overline{JK}\) and \( \overline{HJ}\) is a transversal), and \( \overline{HJ}\cong\overline{HJ}\) (Reflexive Property of Congruence).

Step2: Recall the congruence postulates

The Side - Angle - Side (SAS) postulate states that 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.
In \( \triangle HIJ\) and \( \triangle JKH\), we have:

• \( \overline{JK}\cong\overline{HI}\) (given side)
• \( \angle HJK\cong\angle IHJ\) (angle, which is the included angle between \( \overline{JK},\overline{HJ}\) and \( \overline{HI},\overline{HJ}\) respectively)
• \( \overline{HJ}\cong\overline{HJ}\) (common side)

Answer:

SAS