Question

congruent triangle proofs mixed! complete each proof using the most appropriate method. given: l is the mid - point of $overline{kn}$ and $overline{mp}$ prove: $\triangle mklcong\triangle pnl$ statements reasons 1. l is the midpoint of $kn$ and $mp$ 1. given 2. $overline{kl}congoverline{nl}$ 2. 3. $overline{ml}congoverline{pl}$ 3. 4. $angle mlkcongangle pln$ 4. 5. $\triangle mklcong\triangle pnl$ 5.

Explanation:

Step1: Reason for $KL\cong NL$

Since $L$ is the mid - point of $KN$, by the definition of a mid - point, it divides the segment into two congruent segments. So $KL = NL$, or $KL\cong NL$.

Step2: Reason for $ML\cong PL$

As $L$ is the mid - point of $MP$, by the definition of a mid - point, it divides the segment into two congruent segments. So $ML = PL$, or $ML\cong PL$.

Step3: Reason for $\angle MLK\cong\angle PLN$

$\angle MLK$ and $\angle PLN$ are vertical angles. Vertical angles are always congruent.

Step4: Reason for $\triangle MKL\cong\triangle PNL$

We have $KL\cong NL$, $\angle MLK\cong\angle PLN$, and $ML\cong PL$. By the Side - Angle - Side (SAS) congruence postulate, which states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent, we can conclude that $\triangle MKL\cong\triangle PNL$.

Answer:

1. Definition of mid - point; 3. Definition of mid - point; 4. Vertical angles are congruent; 5. Side - Angle - Side (SAS) congruence postulate