Question

8
given: $overline{hj} \parallel overline{lk}$, $overline{hl} \parallel overline{jk}$
prove: $\triangle hkl \cong \triangle khj$

statements	reasons
2.	2. alternate interior angles
3. $angle jkh \cong angle lhk$	3.
4.	4. reflexive property
5. $\triangle hkl \cong \triangle khj$	5.

Explanation:

Step1: State given parallel sides

$\overline{HJ} \parallel \overline{LK}$, $\overline{HL} \parallel \overline{JK}$

Step2: Identify congruent alternate interior angles

$\angle JHK = \angle LKH$

Step3: Justify alternate interior angles

Alternate Interior Angles

Step4: State congruent shared side

$\overline{HK} = \overline{KH}$

Step5: Apply ASA congruence rule

$\triangle HKL \cong \triangle KHJ$

Answer:

Filled-in two-column proof:

Statements	Reasons
2. $\boldsymbol{\angle JHK \cong \angle LKH}$	2. Alternate Interior Angles
3. $\angle JKH \cong \angle LHK$	3. Alternate Interior Angles
4. $\boldsymbol{\overline{HK} \cong \overline{KH}}$	4. Reflexive Property
5. $\triangle HKL \cong \triangle KHJ$	5. ASA (Angle-Side-Angle) Congruence Postulate