MNOP is a parallelogram because it has both pairs of opposite sides that are parallel and equal in length. We can use properties of quadrilaterals and geometry to prove shapes are specific types of quadrilaterals. For example, the diagram shows that S is the midpoint of MN, T is the midpoint of NR, so U must be the midpoint of NP. We can prove conjectures about lines and angles using properties we know.

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12. Euclidean Geometry
Grade 10

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Proofs and conjectures
We can use the properties of quadrilaterals and geometry to prove that a quadrilateral is a
specific type of quadrilateral.
We can also make conjectures about pairs of lines and angles.
For example: Prove MNOP is a parallelogram in the figure below.

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Proofs and conjectures
For example: In the diagram below S is the mid-point of MN and T is the mid-point of NR.
Prove U is the mid-point of NP.

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