4. 4
INTRODUCTION
Natural resources occur naturally within environments that
exist relatively undisturbed by humanity, in a natural form.
A natural resource is often characterized by amounts of
biodiversity and geodiversity existent in various
ecosystems. In geometry, two figures or objects are
congruent if they have the same shape and size, or if one
has the same shape and size as the mirror image of the
other. Two geometrical objects are called similar if they
both have the same shape, or one has the same shape as
the mirror image of the other.
CONTENT
5. 5
In elementary geometry the word congruent is often used
as follows. The word equal is often used in place of
congruent for these objects.
Two line segments are congruent if they have the same
length.
Two angles are congruent if they have the same
measure.
Two circles are congruent if they have the same
diameter
.
If two objects are similar, each is congruent to the result
of a uniform scaling of the other.
In this figuer they are congruent
6. 6
Orange
Determining congruence of
polygons
For two polygons to be congruent, they must have an
equal number of sides (and hence an equal number—the
same number—of vertices). Two polygons with n sides
are congruent if they each have numerically identical
sequences (even if clockwise for one polygon and
counterclockwise for the other) side-angle-side-angle-...
for n sides and n angles.
Congruence of polygons can be established graphically as
follows:
First, match and label the corresponding vertices of the
two figures.
7. 7
Second, draw a vector from one of the vertices of the
one of the figures to the corresponding vertex of the
other figure. Translate the first figure by this vector so
that these two vertices match.
Third, rotate the translated figure about the matched
vertex until one pair of corresponding sides matches.
Fourth, reflect the rotated figure about this matched
side until the figures match.
If at anytime the step cannot be completed, the polygons
are not congruent.
Similarity
Two geometrical objects are called similar if they both have
the same shape, or one has the same shape as the mirror
image of the other. For example, all circles are
similar to each other, all squares are similar to each other,
and all equilateral triangles are similar to each other. On the
other hand, ellipses are not all similar to each other,
rectangles are not all similar to each other, and isosceles
triangles are not all similar to each other.
Two
geometrical
objects are
called
similar if
they both
have the
same shape,
or one has
the same
shape as the
mirror
Two
geometr
ical
objects
are
called
similar if
they
both
have the
same
8. 8
These are similar circle.
Orange
If two angles of a triangle have measures equal to the
measures of two angles of another triangle, then the
triangles are similar. Corresponding sides of similar
polygons are in proportion, and corresponding angles of
similar polygons have the same measure.
Figures shown in the same color are similar
9. 9
Conclusion
Two triangles are congruent if their corresponding sides are
equal in length and their corresponding angles are equal in
size. Either object can be rescaled, repositioned, and
reflected, so as to coincide precisely with the other object.
If two objects are similar, each is congruent to the result of
a uniform scaling of the other. Two geometrical objects are
called similar if they both have the same Two geometrical
objects are called similar if they both have the same shape,
or one has the same shape as the mirror image of the other,
or one has the same shape as the mirror image of the other.
