ABCD is a quadrilateral in which AB = CD and AD=BC. Show that it is a
parallelogram. Hint: Draw one of the diagonals.]
192
Answers
Answered by
7
Step-by-step explanation:
Given:In □ABCD
AB=DCandAD=BC
To prove: ABCD is a parallelogram
Construction: Draw diagonal AC and DB.
Proof: in △ABC and △ADC
AD=BC [Given]
AB=DC [Given]
AC=AC [Common side]
∴ By SSS property
△ADC≅△ACB
∴∠DAC=∠DCA
∴AB∣∣DC [By theorem]
In△ABDand△DCB
DB=DB [Common side]
AD=BC [Given]
AB=DC [Given]
∴△ABD≅△DCB
∴AD∣∣BC
Since AB∣∣DC and AD∣∣BC.
△ABCD is parallelogram
OK MY FRIEND.
PLEASE MARK TO BRAIN LIST.
Similar questions