# Synthetic and analytical proof: parrallelogram

Theorem: If the consecutive midpoints of the sides of a parallelogram are joined in order, then the quadrilateral formed from the midpoints is a parallelogram.

A. Prove the theorem given above in Euclidean geometry using synthetic techniques.

1. Include each step of your proof.

2. Provide written justification for each step of your proof.

B. Prove the theorem given above in Euclidean geometry using analytic techniques.

1. Include each step of your proof.

2. Provide written justification for each step of your proof.

https://brainmass.com/math/geometry-and-topology/synthetic-and-analytical-proof-parrallelogram-582307

#### Solution Preview

Synthetic Proof (without coordinates)

A P B

*- - - -*- - - - - -*

/ * * /

/ * * /

/ * * /

S * * Q

/ * * /

/ * * /

/ ...

#### Solution Summary

This solution offers all steps and justifications for proving a geometric theorem, both by synthetic and analytical method.