Points A and B are on the side XY of triangle XYZ with XA=AB=BY . Points C and D are on the sides YZ and XZ respectively such that ABCD is a rhombus . Prove that angle XYZ is 90 degree .
Hello, thereddevils!
Please check the wording of the problem.
As stated, the conclusion cannot be true.
Points and are on the side of with
Points and are on the sides and resp. such that is a rhombus.
Prove thatSupposeCode:X o |\ | \ | \ | \ | \ A o \ | * \ | * \ | * \ | * \ | *\ B o o D | * |\ | * | \ | * | \ | * | \ | * | \ Y o - - - - - o - - o Z C
We are given: .
Since is a rhombus: .
Hence: .
Then we have right triangle in which side
. . and hypotenuse are equal. ??
Hello, thereddevils!
It should be: prove that . . . . Ah, got it!
Code:X o |\ | \ | \ | \ | \ | o A | / \ | / θ \ | / \ | / \ |/ \ D o o B |\ / \ | \ / θ \ | \ / \ | \ / \ | \ / \ Z o - - o - - - - - o Y C
We have: .
Let
Since is isosceles,
Then: .
Since
Since is isosceles:
Then: .
In . . . They are complementary!
Therefore: .