Question

Poins A and B are on the same side of a line l. AM and BN are perpendiculars to the line
L. If C is the mid-points of AB, then prove that CM = CN



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Answer 1

Answer:

sis here is your answer

Explanation:

ANSWER

line AD⊥ line ℓ (given)

line BE⊥ line ℓ (given)

Draw line CM⊥ line ℓ .....(I)

lines AD∥CM∥BE

AC=CB (given (since C is mid point AB)

Since CM, is traversal to lines AD and BE

Hence, we can say that DM=ME ......(II)

In ΔDCM and ΔMCE

DM=ME from.....(II)

CM is the common line (common side)

∠DMC=∠EMC=90

o

from.....(I)

So, ΔDCM≅ΔMCE (SAS congruence criteria)

So,

CD=CE by cpct

Hence proved

Answer 2

Answer:

line AD⊥ line ℓ (given)

line BE⊥ line ℓ (given)

Draw line CM⊥ line ℓ .....(I)

lines AD∥CM∥BE

AC=CB (given (since C is mid point AB)

Since CM, is traversal to lines AD and BE

Hence, we can say that DM=ME ......(II)

In ΔDCM and ΔMCE

DM=ME from.....(II)

CM is the common line (common side)

∠DMC=∠EMC=90

o

from.....(I)

So, ΔDCM≅ΔMCE (SAS congruence criteria)

So,

CD=CE by cpct

Hence proved