Congruence and Similarity

Hong Kong

Stage 1 - Stage 3

In the diagram, $NOPQ$`N``O``P``Q` is a parallelogram. Triangles $\triangle NQR$△`N``Q``R` and $\triangle POR$△`P``O``R` are congruent.

a

Which side in $\triangle POR$△`P``O``R` corresponds to side $QR$`Q``R`?

$PR$`P``R`

A

$OR$`O``R`

B

$PO$`P``O`

C

b

If $NR$`N``R` is $4$4 cm long, how long is $PR$`P``R`?

c

The diagonals of a parallelogram:

bisect one another.

A

bisect the corner angles.

B

are equal in length.

C

Easy

Approx a minute

The figure shows quadrilateral $ABCD$`A``B``C``D` , such that $AB$`A``B` is parallel to $CD$`C``D`

and $AD$`A``D` is parallel to $BC$`B``C`.

Consider the parallelogram $ABCD$`A``B``C``D`. We want to deduce a property of the diagonals of a parallelogram.

In parallelogram $ABCD$`A``B``C``D`, $AB$`A``B` is parallel to $DC$`D``C` and $BC$`B``C` is parallel to $AD$`A``D`.

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