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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 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 class=

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nobillionaireNobley
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
TheDemanded

Answer:

Triangle CBE =~ Triangle CDA by HL    b/c hypotenuse, leg and right angle =~

Triangle BFA =~ Triangle DFE by SAS   b/c side, angle, side are =~

Triangle CBF =~ Triangle CDF by SSS   b/c side, side, side are =~

Plus, I got it correct on the quiz :)

Step-by-step explanation:

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