PCH2: Plane Geometry Flashcards
Symbol for “is parallel to”
||
symbol for “is perpendicular to”
|
____
symbol for “is congruent to”
triangle of ABC
∆ ABC
therefore
.
. .
because
. .
.
Right angle
= 90˚
collinear points
lie on the same line
concurrent lines
pass through same point
produced
continued
angles of a straight line
= 180˚
vertically opposite angles
equal
angles at a point
= 360˚
co-interior angles
= 180˚
angle sum of triangle
= 180˚
exterior angle of triangle
= sum of interior opposite angles
angle sum of quadrilateral
= 360˚
angle sum of polygon
S = (n-2) x 180˚
exterior angles of a polygon
= 360˚
exterior angle
180˚ - interior angle
OR
360˚ ÷ number of sides
interior angle
180˚ - exterior angle
number of sides
360˚ ÷ exterior angle
or
angle sum ÷ interior angle
congruent triangles
exactly the same shape and size
tests for congruent triangles
- SSS (all sides equal)
- SAS (2 sides and included angle equal)
- AAS (2 angles and a side of one equal)
- RHS (contains right angle, equal hypotenuse and one other side equal)
isosceles triangle
two equal sides and two equal angles
equilateral triangle
all sides and angles equal
parallelogram
- opposite sides equal
- opposite angles equal
- diagonals bisect each other
rhombus
- opposite sides equal
- opposite angles equal
- diagonals bisect each other at right angles
- diagonals bisect the angles through which they pass
rectangle
- opposite sides equal
- opposite angles equal
- diagonals bisect each other
- diagonals equal
square
- all sides equal
- all angles equal
- diagonals bisect each other
- diagonals are equal
similar triangles
exactly the same shape, but not necessarily the same size
corresponding angles are equal, corresponding sides are in proportion
tests for similar triangles
- corresponding angles are equal or two pairs of corresponding angles are equal
- corresponding sides are proportional (same ratio)
- two pairs of corresponding sides are proportional and the included angles are equal
- hypotenuse and one side of a right-angled triangle are proportional to the the hypotenuse and side of another right-angled tirangle
properties of similar triangles
- a line parallel to one side of a triangle divides the other two sides in proportion
- a line joining the midpoints of two sides of a triangle is parallel to the third side and half its length
intercept properties of transversals to parallel lines
- parallel lines preserve the ratio of intercepts on transversals
pythagoras therom
c^2 = a^2 + b^2
area of a rectangle
A = lb
area of a triangle
A = 0.5 x b x h
area of a parallelogram
A = b x perpendicular height
area of a rhombus
A = 0.5 x xy
area of a trapezium
A = h ÷ 0.5 x (a + b)
area of a square
A = s^2
complementary angles
add up to 90˚
supplementary angles
add up to 180˚
How do you tell if a triangle is right angled?
Sub values for sides into formula for pythagoras
