Question

4 finish the triangle proof by dragging the correct reasons to their box. there will be two extra unused reasons! given: △def and △hgf are right triangles, eg and dh bisect each other at f prove ∠edf ≅ ∠ghf 1. △def and △hgf are right triangles 2. eg and dh bisect each other at f 3. ef = gf 4. df = hf 5. △def ≅ △hgf 6. ∠edf ≅ ∠ghf aas sas definition of bisect given definition of bisect hl vertical angles given cpctc

Explanation:

Step1: First statement

The first statement is given in the problem, so the reason is "Given".

Step2: Second statement

The second statement is also given in the problem, so the reason is "Given".

Step3: Third statement

Since \(EG\) is bisected at \(F\) (from statement 2), by the definition of bisect \(EF = GF\).

Step4: Fourth statement

Since \(DH\) is bisected at \(F\) (from statement 2), by the definition of bisect \(DF=HF\).

Step5: Fifth statement

We have two right - triangles (\(\triangle DEF\) and \(\triangle HGF\)), \(EF = GF\), \(DF = HF\) and \(\angle EFD=\angle HFG\) (vertical angles). So, \(\triangle DEF\cong\triangle HGF\) by \(SAS\) (Side - Angle - Side: the right angle is the included angle between the two sides \(EF, DF\) for \(\triangle DEF\) and \(GF, HF\) for \(\triangle HGF\)).

Step6: Sixth statement

Since \(\triangle DEF\cong\triangle HGF\), then \(\angle EDF\cong\angle GHF\) by \(CPCTC\) (Corresponding Parts of Congruent Triangles are Congruent).

Answer:

1. Given
2. Given
3. Definition of Bisect
4. Definition of Bisect
5. SAS
6. CPCTC