Congruence and Similarity (II) 9.35
More about the Properties of Congruent Figures
In fact, for congruent polygons, all their corresponding lengths
(e.g. heights, diagonals, perimeters) are equal.
e.g. For congruent trapeziums X and Y on the right,
(a) h1 = h2
(b) k1 = k2
(c) p1 = p2
Likewise, for congruent figures involving curves such as circles and
semi-circles, all their corresponding lengths (e.g. diameters, perimeters)
are also equal.
e.g. For congruent semi-circles F and G on the right,
(a) d1 = d2
(b) s1 = s2
k1
h1 p1
k2
h2 p2
trapezium X trapezium Y
X and Y have equal corresponding heights.
◀ X and Y have equal corresponding diagonals.
◀ X and Y have equal perimeters.
◀
semi-circle F semi-circle G
d1
s1
d2
s2
F and G have equal diameters.
◀ F and G have equal perimeters.
◀
In Fig. 1, when a lifting platform is working, the
lengths of the sides of the frame (the green part)
remain unchanged, but the shape changes.
In Fig. 2, when the handle of a suitcase is extended,
the sizes of the interior angles of the quadrilateral
formed (the orange part) remain unchanged, but the
shape changes.
Fig. 1
Fig. 2
This illustrates that the shape of a quadrilateral
cannot be determined when only the lengths of
four sides are given.
i.e. SSSS is not a condition for quadrilaterals to be
congruent.
#retractable structure
This illustrates that the shape of a quadrilateral
cannot be determined when only the sizes of
four angles are given.
i.e. AAAA is not a condition for quadrilaterals to
be congruent.
ET MS
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