Given: MQ = NQ; Q is the midpoint of LP; LM ≅ PN Triangles M L Q and N P Q are connected at point Q. A line is drawn from points M to N to form triangle M N Q. Which congruence theorem can be used to prove △MLQ ≅ △NPQ?
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Given : MQ = NQ; Q is the midpoint of LP; LM ≅ PN Triangles M L Q and N P Q are connected at point Q.
To Find : Which congruence theorem can be used to prove △MLQ ≅ △NPQ
Solution:
Comparing △MLQ and △NPQ
ML = NP ( as given LM ≅ PN )
LQ = PQ (∵ Q is the midpoint of LP)
MQ = NQ Given
=> △MLQ ≅ △NPQ using SSS criteria
SSS - Side Side Side
Corresponding sides of triangles are equal
SSS Congruence theorem can be used to prove △MLQ ≅ △NPQ
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