Question

Drag and drop a statement or reason to each box to complete the proof.

Given: parallelogram EFGH

Prove: EG¯¯¯¯¯ bisects HF¯¯¯¯¯¯ and HF¯¯¯¯¯¯ bisects EG¯¯¯¯¯.

Parallelogram E F G H with diagonals E G and H F intersecting at point K.

Put responses in the correct response input area to answer the question. Select a response, navigate to the desired input area and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Statement Reason
parallelogram EFGH
Given
EF¯¯¯¯¯≅HG¯¯¯¯¯¯
Press enter key to drop response here.Response input area
EF¯¯¯¯¯∥HG¯¯¯¯¯¯
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Press enter key to drop response here.Response input area Press enter key to drop response here.Response input area
△EKF≅△GKH
ASA Congruence Postulate
Press enter key to drop response here.Response input area CPCTC
EG¯¯¯¯¯
bisects HF¯¯¯¯¯¯
and HF¯¯¯¯¯¯
bisects EG¯¯¯¯¯
. Definition of bisector

Answer 1

Fill the blanks as follows:

1. Statement: EF ≅ HG
Reason: Opposite sides of a parallelogram are congruent

2. Statement: EF ∥ HG
Reason: Opposite sides of a parallelogram are parallel

3. Statement: ∠KEF ≅ ∠KGH and ∠EFK ≅ ∠GHK
Reason: If lines are parallel, corresponding (or alternate interior) angles are congruent

4. (Given) △EKF ≅ △GKH — ASA Congruence Postulate

5. Statement: EK ≅ KG and KF ≅ KH
Reason: CPCTC

6. Statement: EG bisects HF and HF bisects EG
Reason: Definition of bisector

These complete the proof that the diagonals bisect each other in parallelogram EFGH.