Question

Can someone please help me

Answer 1

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Answer:

  B.  DH ≅ JF

Step-by-step explanation:

You are given congruence of one side and an angle at the end of that side. To prove the triangles are congruent, you need another side (on the other side of the angle), or you need the angle at the other end of the given side.

The answer choices are all about segments, so the one that is applicable is the one relating corresponding parts of segment DJ:

  DH ≅ JF

_____

HF can be added to both those parts to show that DF ≅ JH, the missing piece for the use of the SAS congruence theorem.

Answer 2

Answer:

Option B)  DH = JF

Step-by-step explanation:

Since we are given that sides ED and IJ are equal, and that also angles <D and <J are equal in measure, since both angles share the segment HF,

then if DH = FJ,

adding this segment HF to both sides of the equation above, we get:

DH + HF = HF + FJ

which totals

DF = HJ

making this a new equality between sides, and leading to a SAS case for congruency (two equal sides, and the angle in between them equal).