Provide reasons for the proof of the triangle proportionality theorem

1. KL || MN  given

2. angle JKL cog angle JMN and angle JLK cong JNM    These are corresponding angles on a traversal of parallel lines.

3. Triangle JKL similar to triangle JMN     angle angle similarlity

4. JM/JK = JN/JL     Proportionality of corresponding parts of similar triangles

5. JM=JK+KM and JN=JL+LN  Collinear segment addition postulate

6. (JK+KM)/JK = (JL+LN)/JL    Substitution

7.  ... addition of fractinos

8. ... simplify

9.  KM/JK = LN/JL        Simplify (or Subtraction something)

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

the answer is $42.96

step-by-step explanation: