Geometry Abbreviations at SBHS
1.
Symbols can be used in the abbreviation if they read correctly.
e.g. or for angle but NOT || for parallel e.g. AB and CD are || lines is incorrect.
2.
Conventional abbreviations are allowed.
e.g. ext.
int.
opp.
quad.
Pythag.
However abbreviations of the type (i) v.o.a. for vertically opposite angles
(ii) ||-gram for parallelogram
are NOT acceptable.
3.
If parallel lines are labelled in the diagram, use their names in the reason.
e.g.
co-interior angles, AB || PQ
NOT co-interior angles in parallel lines
4.
Begin algebraic statements with a sum or a product if the theorem
refers to a sum or a product.
e.g.
x + 110 = 180
(angle sum of triangle)
NOT x = 180 110
(angle sum of triangle)
5.
Theorems can be abbreviated by using the distinctive words found only
within their enunciation, i.e. the particular words used in their statement
e.g. The square of a tangent to a circle from an external point is equal to the product of the
intercepts of any secant from the point.
This can be abbreviated as:square of the tangent OR
intersecting tangent and secant OR
tangent and secant
Theorem
Abbreviation
1.
Angles on a straight line are supplementary.
2.
Vertically opposite angles are equal.
vertically opposite angles
3.
4.
The sum of angles at a point is 360.
When lines are parallel:
alternate angles are equal;
angles at a point
alternate angles in parallel lines
corresponding angles are equal;
corresponding angles in parallel lines
co-interior angles are supplementary;
co-interior angles in parallel lines
and conversely.
alternate angles are equal OR
corresponding angles are equal OR
co-interior angles are supplementary.
5.
If two lines are parallel to a third line, then
they are parallel to one another.
6.
The sum of the interior angles of a triangle
is 180.
The exterior angle of a triangle is equal to
the sum of the two interior opposite angles.
If three sides of a triangle are equal then
each interior angle is 60.
7.
8.
straight line OR straight angle
parallel to third line
angle sum of triangle
exterior angle of triangle
equilateral triangle
Theorem
9.
Each angle of an equilateral triangle is
equal to 60.
10.
11.
12.
Abbreviation
equilateral triangle
If two sides of a triangle are equal, then the
angles opposite the equal sides are equal.
angles opposite equal sides in a triangle
Conversely, if two angles of a triangle are
equal, then the sides opposite those angles
are equal.
sides opposite equal angles in a triangle
In any right angled triangle, the square on
the hypotenuse is equal to the sum of the
squares on the other two sides.
Pythagoras Theorem
If the square on one side of a triangle
equals the sum of the squares on the other
two sides, then the angle between these
other two sides is a right angle.
The sum of the interior angles of any
quadrilateral is 360.
The sum of the exterior angles of any
convex polygon is 360.
14.
Congruence of triangles:
a) If three sides of one triangle are
respectively equal to three sides of another
triangle, then the two triangles are
congruent.
13.
converse of Pythagoras Theorem
angle sum of quadrilateral
exterior angle sum of polygon
SSS
b) If two sides and the included angle of one
triangle are respectively equal to two sides
and the included angle of another triangle,
then the two triangles are congruent.
SAS
c) If two angles and one side of one triangle
are respectively equal to two angles and the
AAS
matching side of another triangle, then the
two triangles are congruent.
d) If the hypotenuse and a second side of one
right-angled triangle are respectively equal
to the hypotenuse and a second side of
another right-angled triangle, then the two
triangles are congruent.
15.
RHS
The opposite angles of a parallelogram are
equal.
opposite angles of parallelogram
The opposite sides of a parallelogram are
equal.
opposite sides of parallelogram
The diagonals of a parallelogram bisect
each other.
diagonals of parallelogram
Theorem
Abbreviation
The diagonals of a rhombus bisect each
other at right angles.
diagonals of rhombus
The diagonals of a rhombus bisect the
vertex angles through which they pass.
diagonals of rhombus bisect angles
17.
The diagonals of a rectangle are equal.
diagonals of rectangle
18.
If both pairs of opposite angles of a
quadrilateral are equal, then it is a
parallelogram.
If both pairs of opposite sides of a
quadrilateral are equal, then it is a
parallelogram.
16.
2 pairs opposite angles equal
2 pairs opposite sides equal
If one pair of opposite sides of a
one pair of opposite sides both equal and
quadrilateral is both equal and parallel, then
parallel
it is a parallelogram.
If all sides of a quadrilateral are equal, then
it is a rhombus.
20.
Similarity of triangles:
a) If the three sides of one triangle are
proportional to the three sides of another
triangle, then the two triangles are similar.
19.
all sides equal
3 pairs of corresponding sides in
proportion
b) If two sides of one triangle are proportional
to two sides of another triangle, and the
included angles are equal, then the two
triangles are similar.
2 pairs of corresponding sides in
proportion and included angles equal
c) If two angles of one triangle are
respectively equal to two angles of another
triangle, then the two triangles are similar.
equiangular
d) If the hypotenuse and a second side of a
right-angled triangle are proportional to the
hypotenuse and a second side of another
right-angled triangle, then the two triangles
are similar.
21.
22.
The interval joining the midpoints of two
sides of a triangle is parallel to the third side
and half its length.
Conversely, the line through the midpoint
of a side of a triangle parallel to another
side bisects the third side.
Parallel lines preserve ratios of intercepts
on transversals.
hypotenuse and side in proportion
join of midpoints
converse of join of midpoints
parallel lines preserve ratios
