Question

10. In the adming figure, ABCD is a parallelogram. Find and x,y,z,w​

Answer 1

Answer:

In △AXD and △CYB

∠ADX=∠CBY [Alternate interior angle ]

AD=CB [Opposite sides of parallelogram ABCD]

DX=BY [Given]

∴△AXD≅△CYB [Using SAS congruence]

∴AX=CY [By CPCT]

Now,

In △AYB and △CXD

∠ABY=∠CDX [Alternate interior angle ]

AB=CD [Opposite sides of parallelogram ABCD]

DX=BY [Given]

∴△AYB≅△CXD [Using SAS congruence]

∴AY=CX [By CPCT]

From the result we obtained AX=CY and AY=CX

Since opposite sides quadrilateral AXCY are equal to each other

Therefore, AXCY is a parallelogram