Question

3. Complete the proof below.


Help please!!!

Answer 1

The completed proof is presented as follows;

The two column proof is presented as follows;

Statements
`{}` Reason

1.
`\overline {HI}` ║
`\overline {KL}`, J is the midpoint of
`\overline {HL}`
`{}` 1. Given

2. ∠IHJ ≅ ∠JLK
`{}` 2. Alternate angles are congruent

3. ∠IJH ≅ ∠KJL
`{}` 3. Vertically opposite angles

4.
`\overline {HJ}` ≅
`\overline {JL}`
`{}` 4. Definition of midpoint

5. ΔHIJ ≅ ΔLKJ
`{}` 5. By ASA rule of congruency

Explanation:

Alternate angles formed by the crossing of the two parallel lines
`\overline {HI}` and
`\overline {KL}`, by the transversal
`\overline {HL}` are equal

Vertically opposite angles formed by the crossing of two straight lines
`\overline {IK}` and
`\overline {HL}` 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
`{}` in ΔLKJ and ∠IJH in ΔHIJ ≅ ∠KJL in ΔLKJ, and that the included sides between the two congruent angles is also congruent
`\overline {HJ}` ≅
`\overline {JL}`, then the two triangles are congruent, ΔHIJ ≅ ΔLKJ.