Given: ∠bcd is right; bc ≅ dc; df ≅ bf; fa ≅ fe which relationships in the diagram are true? check all that apply.
△acf ≅ △ecf by hl
△cbf ≅ △cdf by sss
△bfa ≅ △dfe by sas
△cfd ≅ △efd by sss
△cbe ≅ △cda by hl

Given that B C ≅ D C and D F ≅ B F. Also, C F ≅ C F by refrexive property.

Therefore, △ C B F ≅ △ C D F by S S S

Given that F A ≅ F E
i.e. A F ≅ E F
Also, given that D F ≅ B F
i.e. F D ≅ F B

This means that A F + F D ≅ E F + F B which means that A D ≅ E B

Now, given that ∠ B C D is right, this means that △ C B E is a right triangle with the right angle at C and E B as its hypothenus. Also △ C D A is a right triangle with the right angle at C and A D as its hypothenus.

Thus, given that A D ≅ E B and the legs B C ≅ D C, therefore, △ C B E ≅ △ C D A by H L.

Therefore, the true statements are:
△CBF ≅ △CDF by SSS, and

△CBE ≅ △CDA by HL

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