Question

CHAPTER - 7 TRIANGLES
14. In the figure, ABCD is a square. X, Y and Z are the points
is a square. X, Y and Z are the points in AB, BC and CD respectively
such that AX = BY = CZ. Prove that-
i. XY = YZ
ii. _XYZ = 90°
45°​

Answer 1

Answer:

GIVEN=AX=BY=CZ

(1)=AB=BC=CD

BY+YC=AX+XB

XB=YC

InTriangleXBY AND ZCY

XB=YC

BY=CZ

Angle XBY=ANGLE YCZ(90)

TRIANGLE XBY=TRIANGLE ZCY

ZY=XY(CPCT)

ANGLE(BXY=CYZ)

ANGLE(BYX=YZC)

ANGLE(BYX+BXY=90)

ANGLE(BYX+CYZ=90)

ANGLE(BYX+XYZ+CYZ=180)

ANGLE(90+XYZ=180)

ANGLE(XYZ=180-90)

ANGLE(XYZ=90)