QUESTION $1$

$1\mathrm{.}1$ A parallelogram is defined as a quadrilateral in which both pairs of opposite sides are parallel. What pre$-$knowledge concepts would Grade $10$ learners need to know before learning parallelogram theorems?

$1\mathrm{.}2$ ABCD is a parallelogram with $A\frac{B}{\frac{?}{?}}CD$ and $A\frac{D}{\frac{?}{?}}BC.$ Show that

$1\mathrm{.}2\mathrm{.}1AB=CD$ and $AD=BC$

$1\mathrm{.}2\mathrm{.}2$ hat$(A)=$hat$(C)$ and hat$(B)=$hat$(D)$

$1\mathrm{.}2\mathrm{.}3$ Design a memorandum from a mathematics$-$based perspective. You should carefully think through the allocation of the marks. Please present your work neatly and for each mark that you give in the solution, give a reason$/$explanation$,$ so that somebody else who marks the problem according to your memorandum will understand clearly for what the marks are allocated.

$1\mathrm{.}3$ Misconceptions are often discarded as mistakes.

$1\mathrm{.}3\mathrm{.}1$ Give FOUR examples of misconceptions that learners might have in response to question $1\mathrm{.}2.$

$1\mathrm{.}3\mathrm{.}2$ Discuss how you would help a learner to remedy the misconceptions that you have mentioned in question $1\mathrm{.}3\mathrm{.}1.$

$(3)$

$[30]$