Question

In an isosceles trapezoid the diagonals are congruent (true or false)

Answer 1

Let ABCD be the trapezium with AB || CD, AB < DC and AD = BC.
From B drop a perpendicular to meet CD at P.
From A drop a perpendicular to meet CD at Q.

In the triangles BPC, AQD:
BP = AQ (opposite sides of rectangle ABPD)
BC = AD (given)
Angle BPC = angle AQD (both 90deg)
Therefore triangles BPC and AQD are congruent (RHS), and in particular angle CBP = angle DAQ .....(1)

Angle DAB = angle DAQ + angle QAB
= angle DAQ + 90deg
Angle CBA = angle CBP + angle PBA
= angle CBP + 90deg
Therefore from (1):
Angle DAB = angle CBA .......(2)

In the triangles ABC, BAD:
AB = BA (common)
BC = AD(given)
Angle CBA = angle DAB (proved (2))
Therefore triangles ABC, BAD are congruent, and in particular AC = BD.

Answer 2

So True.

Answer 3

thank you sooooo muchhhh !!!!

Answer 4

true

Answer 5

true @angelacuevas