Question

IN THE FIGURE, ABCD IS A RECTANGLE. SHOW THAT :
(A) AC = BD
(B) TRIANGLE DAB =~ TRIANGLE BCD
(C) TRIANGLE DAB =~ TRIANGLE CBA
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Answer 1

Answer:

ABCD is a rectangle.

therefore, AB=CD and AD=BC

(A) AC=BD ( since diagonals of a rectangle are equal)

(B) In tri DAB and tri BCD

AD=BC (proved above)

AB=CD (proved above)

BD=BD (common)

tri DAB=~tri BCD (by sss congruency)

(C) In tri DAB and tri CBA

AD=AC (proved above)

AB=AB (common)

angle DAB=angle CBA (each 90°)

tri DAB=~ tri CBA (by ASA congruency)

Hope this will help you.