In the given figure ABCD is a rectangle BM and DN are perpendicular to AC from B and D respectively. Prove that AN =CM
Answers
Step-by-step explanation:
Answer
ABCD is a parallelogram then,
AD∥BC and AC is a transversal.
AD∥BC and AC is a transversal.∴ ∠BCA=∠DAC [ Alternate angles ]
AD∥BC and AC is a transversal.∴ ∠BCA=∠DAC [ Alternate angles ]i.e. ∠BCM=∠DAN ---- ( 1 )
AD∥BC and AC is a transversal.∴ ∠BCA=∠DAC [ Alternate angles ]i.e. ∠BCM=∠DAN ---- ( 1 )In △BMC and △DNA
AD∥BC and AC is a transversal.∴ ∠BCA=∠DAC [ Alternate angles ]i.e. ∠BCM=∠DAN ---- ( 1 )In △BMC and △DNA⇒ BC=AD [ Opposite sides of parallelogram are equal ]
AD∥BC and AC is a transversal.∴ ∠BCA=∠DAC [ Alternate angles ]i.e. ∠BCM=∠DAN ---- ( 1 )In △BMC and △DNA⇒ BC=AD [ Opposite sides of parallelogram are equal ]⇒ ∠BCM=∠DAN [ From ( 1 ) ]
AD∥BC and AC is a transversal.∴ ∠BCA=∠DAC [ Alternate angles ]i.e. ∠BCM=∠DAN ---- ( 1 )In △BMC and △DNA⇒ BC=AD [ Opposite sides of parallelogram are equal ]⇒ ∠BCM=∠DAN [ From ( 1 ) ]⇒ ∠BMC=∠DNA [ Both 90
AD∥BC and AC is a transversal.∴ ∠BCA=∠DAC [ Alternate angles ]i.e. ∠BCM=∠DAN ---- ( 1 )In △BMC and △DNA⇒ BC=AD [ Opposite sides of parallelogram are equal ]⇒ ∠BCM=∠DAN [ From ( 1 ) ]⇒ ∠BMC=∠DNA [ Both 90 o
AD∥BC and AC is a transversal.∴ ∠BCA=∠DAC [ Alternate angles ]i.e. ∠BCM=∠DAN ---- ( 1 )In △BMC and △DNA⇒ BC=AD [ Opposite sides of parallelogram are equal ]⇒ ∠BCM=∠DAN [ From ( 1 ) ]⇒ ∠BMC=∠DNA [ Both 90 o . ]
AD∥BC and AC is a transversal.∴ ∠BCA=∠DAC [ Alternate angles ]i.e. ∠BCM=∠DAN ---- ( 1 )In △BMC and △DNA⇒ BC=AD [ Opposite sides of parallelogram are equal ]⇒ ∠BCM=∠DAN [ From ( 1 ) ]⇒ ∠BMC=∠DNA [ Both 90 o . ]∴ △BMC≅△DNA [ By SAA congruence rule ]
AD∥BC and AC is a transversal.∴ ∠BCA=∠DAC [ Alternate angles ]i.e. ∠BCM=∠DAN ---- ( 1 )In △BMC and △DNA⇒ BC=AD [ Opposite sides of parallelogram are equal ]⇒ ∠BCM=∠DAN [ From ( 1 ) ]⇒ ∠BMC=∠DNA [ Both 90 o . ]∴ △BMC≅△DNA [ By SAA congruence rule ]∴ BM=DN [ By CPCT ]
Answer:
In triangle BMC and triangle DNA
BC =AD(opposite sides of rectangle are equal)
Angle BCM=Angle MAD(Alternate angles)
Angle BMC =Angle DNA (BM and DN perpendicular to AC)
Therefore triangle BMC congruent to triangle DNA
Therefore BM =DN (cpct)