Download Vertically opposite angles are equal

Geometry reasoning
These geometric properties may be used to calculate the size of angles in geometry problems and then given as the reason for your answer. .
The reasons can be shortened and the accepted abbreviations are shown.
Reason
Vertically
opposite angles
are equal
Adjacent angles
on a straight line
add to 180º
Angles at a point
add to 360º
Abbreviation
vert opp s
Link
Vertically opposite angles
http://www.bbc.co.uk/scotland/education/bitesize/standard/mathsI/pythagoras/line_angles_facts_rev4.shtml
Adj, s on str.
line
Three Rules about angles and triangles. See Rule 1. http://www.waldomaths.com/Angle1.jsp
s at pt
Simple angle facts http://www.bbc.co.uk/schools/gcsebitesize/maths/shape/anglesrev2.shtml
Right angles, straight angles and full turns
http://www.bbc.co.uk/scotland/education/bitesize/standard/mathsI/pythagoras/line_angles_facts_rev2.shtml
Angle sum at a point, on a line, in a triangle and in a quadrilateral
http://www.bbc.co.uk/schools/ks3bitesize/maths/shape_and_space/angles_1_5.shtml
Angles in a
triangle add to
180º
 sum of Δ
The Different Types of Triangle
http://www.bbc.co.uk/scotland/education/bitesize/standard/mathsI/pythagoras/line_angles_facts_rev5.shtml
Three Rules about angles and triangles. See Rule 2. http://www.waldomaths.com/Angle1.jsp
The exterior
angle of a
triangle equals
the sum of the
two interior
opposite angles
ext  of Δ
Angle properties of triangles
http://www.bbc.co.uk/schools/gcsebitesize/maths/shapeih/straightlinesanglesandpolygonsrev2.shtml
Three Rules about angles and triangles,. See Rule 3. http://www.waldomaths.com/Angle1.jsp
The base angles
of an isosceles
triangle are
equal
base s isos. Δ
The angle sum
of an isosceles
triangle is 180º
 sum isos. Δ
The different types of triangle
http://www.bbc.co.uk/scotland/education/bitesize/standard/mathsI/pythagoras/line_angles_facts_rev5.shtml
Each angle in an
equilateral
triangle is 60º
 in equilat. Δ
The different types of triangle
http://www.bbc.co.uk/scotland/education/bitesize/standard/mathsI/pythagoras/line_angles_facts_rev5.shtml
Corresponding
angles on
parallel lines are
equal
corresp s, //
lines
Parallel lines http://www.bbc.co.uk/schools/gcsebitesize/maths/shape/anglesrev4.shtml
Angles made by parallel lines
http://www.bbc.co.uk/scotland/education/bitesize/standard/mathsI/pythagoras/line_angles_facts_rev3.shtml
Angles in parallel lines http://www.waldomaths.com/Angle2.jsp
Alternate angles
on parallel lines
are equal
alt. s, // lines
Co-interior
angles on
parallel lines are
supplementary
(add to 180º)
co-int s, //
lines
Parallel lines http://www.bbc.co.uk/schools/gcsebitesize/maths/shape/anglesrev4.shtml
Angles made by parallel lines
http://www.bbc.co.uk/scotland/education/bitesize/standard/mathsI/pythagoras/line_angles_facts_rev3.shtml
Angles in parallel lines http://www.waldomaths.com/Angle2.jsp
Parallel lines http://www.bbc.co.uk/schools/gcsebitesize/maths/shape/anglesrev4.shtml
The interior
angles of a
polygon add to
180(n – 2)º,
where n is the
number of sides
int  sum of
polygon
Angle properties of polygons http://www.bbc.co.uk/schools/gcsebitesize/maths/shape/polygonsrev3.shtml
The exterior
angles of a
polygon add to
360
ext  sum of
polygon
Angle properties of polygons http://www.bbc.co.uk/schools/gcsebitesize/maths/shape/polygonsrev3.shtml
The exterior
angle of a
regular polygon
is 360/n degrees
The interior
angle of a
regular polygon
is [180(n-2)]/n
degrees, where n
is the number of
sides
Isosceles
triangle, equal
radii
ext  of
polygon
Calculating the interior and exterior angles of regular polygons
http://www.bbc.co.uk/schools/gcsebitesize/maths/shape/polygonsrev4.shtml
int  of
polygon
Calculating the interior and exterior angles of regular polygons
http://www.bbc.co.uk/schools/gcsebitesize/maths/shape/polygonsrev4.shtml
Calculating the number of sides in a regular polygon, given the interior angle
http://www.bbc.co.uk/schools/gcsebitesize/maths/shapeih/straightlinesanglesandpolygonsrev4.shtmlv
isos Δ, = radii
Isosceles
base s isos Δ,
triangle, equal
= radii
radii and base
angles of
isosceles triangle
are equal
Isosceles
triangle, equal
radii and angles
of a triangle add
to 180º
 sum isos Δ,
= radii
The angle at the
centre is equal to
twice the angle
at the
circumference
on the same arc
 at centre
Angles on the
same arc are
equal
s on same arc
 at centre
 in semicircle
Angle at the centre of a circle is double the size of the angle at the edge
http://www.bbc.co.uk/schools/gcsebitesize/maths/shapeh/circlepropertiesrev2.shtml
Angle at the centre http://www.waldomaths.com/Circle2.jsp
Important facts about circles
http://www.bbc.co.uk/scotland/education/bitesize/standard/mathsI/pythagoras/circle_angles_rev2.shtml
Angle in a semicircle
http://www.bbc.co.uk/schools/gcsebitesize/maths/shapeih/straightlinesanglesandpolygonsrev3.shtml
Opposite angle
of a cyclic
quadrilateral are
supplementary
(add to 180º)
opp s, cyclic
quad
The exterior
angle of a cyclic
quadrilateral is
equal to the
interior opposite
angle
ext , cyclic
quad
Opposite angles in a cyclic quadrilateral add up to 180°
http://www.bbc.co.uk/schools/gcsebitesize/maths/shapeh/circlepropertiesrev4.shtml
Opposite angles of a cyclic quadrilateral http://www.waldomaths.com/Circle1.jsp
The angle where tgt  rad
the radius meets
the tangent is 90º
The angle between the tangent and the radius is 90°
http://www.bbc.co.uk/schools/gcsebitesize/maths/shapeh/circlepropertiesrev5.shtml
Important facts about circles
http://www.bbc.co.uk/scotland/education/bitesize/standard/mathsI/pythagoras/circle_angles_rev2.shtml
Tangents from a
point to a circle
are the same
length
Tangents from a point outside the circle are equal in length
http://www.bbc.co.uk/schools/gcsebitesize/maths/shapeh/circlepropertiesrev6.shtml
equal tangents