Answer:
The completed proof is presented as follows;
The two column proof is presented as follows;
Statements [tex]{}[/tex] Reason
1. [tex]\overline {HI}[/tex] ║ [tex]\overline {KL}[/tex], J is the midpoint of [tex]\overline {HL}[/tex] [tex]{}[/tex] 1. Given
2. ∠IHJ ≅ ∠JLK[tex]{}[/tex] 2. Alternate angles are congruent
3. ∠IJH ≅ ∠KJL [tex]{}[/tex] 3. Vertically opposite angles
4. [tex]\overline {HJ}[/tex] ≅ [tex]\overline {JL}[/tex] [tex]{}[/tex] 4. Definition of midpoint
5. ΔHIJ ≅ ΔLKJ [tex]{}[/tex] 5. By ASA rule of congruency
Step-by-step explanation:
Alternate angles formed by the crossing of the two parallel lines [tex]\overline {HI}[/tex] and [tex]\overline {KL}[/tex], by the transversal [tex]\overline {HL}[/tex] are equal
Vertically opposite angles formed by the crossing of two straight lines [tex]\overline {IK}[/tex] and [tex]\overline {HL}[/tex] are always equal
A midpoint divides a line into two equal halves
Angle-Side-Angle, ASA rule of congruency states that two triangles ΔHIJ and ΔLKJ, that have two congruent angles, ∠IHJ in ΔHIJ ≅ ∠JLK[tex]{}[/tex] in ΔLKJ and ∠IJH in ΔHIJ ≅ ∠KJL in ΔLKJ, and that the included sides between the two congruent angles is also congruent [tex]\overline {HJ}[/tex] ≅ [tex]\overline {JL}[/tex], then the two triangles are congruent, ΔHIJ ≅ ΔLKJ.
