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Drag the statements and reasons to the proper locations in the table. Please list givens first.
Given: LQ NP
Prove: ALMQ APMN
~
L
N
M
0
Statement
P
ALMQ APMN
Justification
Vertical
Angles

View my other questions to see more details on the problem since it could not all be fitted in one image Drag the statements and reasons to the proper locations class=


Answer :

Answer:

[tex]\overline{LQ}\parallel \overline{NP}[/tex], given

∠LMQ ≅ ∠PMN, vertical angles

∠Q ≅ ∠N, alternate interior angles

ΔLMQ ~ ΔPMN, AA~

Step-by-step explanation:

    We know that we need to prove ΔLMQ ~ ΔPMN, in words, the triangle LMQ is similar to triangle PMN.

    It is given that [tex]\overline{LQ}\parallel \overline{NP}[/tex], so we will put given as the first justification with the statement [tex]\overline{LQ}\parallel \overline{NP}[/tex].

    The second thing I notice is the vertical angles. We can prove the statement ∠LMQ ≅ ∠PMN with the justification of vertical angles. Vertical angles will always be congruent. Vertical angles are made by two intersecting lines.

    Since [tex]\overline{LQ}\parallel \overline{NP}[/tex] are two parallel lines, line QN is a transversal. This means that it forms alternate interior angles. With this information, ∠Q ≅ ∠N.

    Finally, we come to proving ΔLMQ ≅ ΔPMN. We have proved that each of the two triangles have two congruent angles, this means they are proved similar by the AA theorem, aka angle-angle. When two triangles have two congruent angles, the third must also be congruent meaning the triangles are similar.