Answer:
See the bolded parts below. It corresponds to the blanks we have to fill in for each step.
Step-by-step explanation:
Taking a look at the figure, we see that KL ║ MN, ( which is given, as you can see ) while MJ and NJ act each as a transversal. This is a key point that will help us.
2. For step 2, we see that ∠JKL ≅ ∠JMN, while ∠JLK ≅ ∠JNM. This is true is they are present as corresponding angles, on either transversal. We can fill in this blank with " Corresponding angles. "
3. Therefore, for this 3rd step triangles JKL and JMN will be similar by " angle angle similarity. " After all, ∠JKL ≅ ∠JMN / ∠JLK ≅ ∠JNM.
4. This step can be proved by the " Proportionality of Corresponding Parts in Similar Triangles. " As you can see, the triangles are similar - and hence their parts correspond to one another.
5. I believe you mean step 5 to be " JM = JK + KM and JN = JL + LN. " That being said this is true by the " Partition Postulate, " which states that a whole is composed of it's parts.
6. This step substituted the 5th step into the 4th step. Therefore, it can be stated as " Substitute step 5 ➡ step 4. "
7. And for this last step here you can say " Simplify further. "
