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. Statement Reason parallelogram EFGH Given EF¯¯¯¯¯∥HG¯¯¯¯¯¯ When two parallel lines are cut by a transversal, alternate interior angles are congruent. The opposite sides of a parallelogram are congruent. △EKF≅△GKH ASA Congruence Postulate CPCTC EG¯¯¯¯¯ bisects HF¯¯¯¯¯¯ and HF¯¯¯¯¯¯ bisects EG¯¯¯¯¯ .

Answer 1

Answer:

The question is incomplete. The complete question has been added as an attachment to the solution.

To aid easy identification of the unknowns, I attached another document where I numbered the unknowns.

1) EF ≅ HG

2) EF || HG

3) <FEK ≅ <HGK

<EFK ≅ <GHK

4) When two parallel lines are cut by a transversal, alternate interior angles are congruent.

5) EK ≅ GK

FK ≅ HK

Step-by-step explanation:

1) In the given parallelogram EFGH,

It is stated that the opposite sides of a parallelogram are congruent. Therefore, EF ≅ HG

2) It would be noted from the properties of a parallelogram, that the opposite sides are parallel. Therefore, EF || HG

3) Definition of a parallelogram: A parallelogram is a quadrilateral with two opposite sides that are parallel and equal in length.

4) One of the properties of a parallelogram states that when two parallel lines are cut by a transversal, alternate interior angles are congruent.

5) It can be seen from the question that △EKF≅△GKH as a result of congruence Postulate.

And the CPCTC proves,

EK ≅ GK

FK ≅ HK

CPCTC means Corresponding Parts of Congruent Triangles are Congruent.

When you have two triangles that have been proven as congruent, then each part of one triangle is equal in size and shape to the corresponding part in the other triangle.