Question

Given: Quadrilateral DEFG is a parallelogram.



Prove: GH ≅ EH
DH ≅ FH

Proof:
Statement Reason
1. Quadrilateral DEFG is a parallelogram. given
2.
definition of a parallelogram
3. Draw and . These line segments are
transversals cutting two pairs of parallel lines:
and and and . drawing line segments
4. Place point H where and intersect. defining a point
5. ∠HGD ≅ ∠HEF
∠HDG ≅ ∠HFE

6. DG ≅ EF Opposite sides of a parallelogram are congruent.
7. ASA criterion for congruence
8. GH ≅ EH
DH ≅ FH Corresponding sides of congruent triangles are congruent.
1
What is the missing statement for step 7 in this proof?
A.
ΔDGH ≅ ΔFEH
B.
ΔGHF ≅ ΔEHD
C.
ΔDGF ≅ ΔFED
D.
ΔDEF ≅ ΔEDG

Answer 1

Answer:

A.  ΔDGH ≅ ΔFEH

Step-by-step explanation:

We are given the proof of GH ≅ EH and DH ≅ FH.

Now, previous to step 7, we have obtained,

Step 5: ∠HGD ≅ ∠HEF  and ∠HDG ≅ ∠HFE

Step 6: DG ≅ EF as opposite sides of a parallelogram are congruent.

Since, we have that two angles of the triangles are congruent and their including sides are also congruent.

Thus, by Step 7 i.e. ASA criterion for congruence, we get that the corresponding triangles are also congruent.

Hence, we get, ΔDGH ≅ ΔFEH.