Question

given: $overline{jk}paralleloverline{lm}$, $overline{jl}paralleloverline{km}$
prove: $\triangle{jkl}cong\triangle{mlk}$
statement

1. $overline{jk}paralleloverline{lm}$, $overline{jl}paralleloverline{km}$
2. $angle{jlk}congangle{mkl}$
3. $angle{jkl}congangle{mlk}$
4. $overline{kl}congoverline{lk}$
5. $\triangle{jkl}cong\triangle{mlk}$

reason
1.
2.
3.
4.
5.
given sss sas aas asa hl definition of midpoint definition of angle bisector reflexive property corresponding angles alternate interior angles vertical angles

Explanation:

Step1: State given information

Given

Step2: Identify alternate - interior angles

Since $\overline{JL}\parallel\overline{KM}$, $\angle{JLK}\cong\angle{MKL}$ by the Alternate Interior Angles.

Step3: Identify alternate - interior angles

Since $\overline{JK}\parallel\overline{LM}$, $\angle{JKL}\cong\angle{MLK}$ by the Alternate Interior Angles.

Step4: Note common side

$\overline{KL}\cong\overline{LK}$ by the Reflexive Property.

Step5: Prove triangle congruence

$\triangle{JKL}\cong\triangle{MLK}$ by the ASA (Angle - Side - Angle) congruence criterion.

Answer:

1. Given
2. Alternate Interior Angles
3. Alternate Interior Angles
4. Reflexive Property
5. ASA