Question

3. Complete the proof below. Help please!!!

Answer 1

Answer:

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

Step-by-step 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.