Mathematics Geometry Examination Guidelines: Triangles, Circles, and Quadrilaterals

A comprehensive set of vocabulary flashcards covering the official geometry examination guidelines for triangles, circles, and quadrilaterals based on the DBE 2014 standards.

Interior angles of a triangle

The interior angles are supplementary, having a sum of $180^{\circ}$.

Exterior angle of a triangle

Equal to the sum of the interior opposite angles.

Isosceles triangle (Angles)

The angles opposite the equal sides in an isosceles triangle are equal.

Isosceles triangle (Sides)

The sides opposite the equal angles in an isosceles triangle are equal.

Theorem of Pythagoras

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Converse Theorem of Pythagoras

If the square of the longest side in a triangle is equal to the sum of the squares of the other two sides, then the triangle is right-angled.

SSS Congruence

If three sides of one triangle are respectively equal to three sides of another triangle, the triangles are congruent.

SAS (or SZS) Congruence

If two sides and an included angle of one triangle are respectively equal to two sides and an included angle of another triangle, the triangles are congruent.

AAS (or ZZS) Congruence

If two angles and one side of one triangle are respectively equal to two angles and the corresponding side in another triangle, the triangles are congruent.

RHS (or 90HS) Congruence

If in two right angled triangles, the hypotenuse and one side of one triangle are respectively equal to the hypotenuse and one side of the other, the triangles are congruent.

Midpoint Theorem

The line segment joining the midpoints of two sides of a triangle is parallel to the third side and equal to half the length of the third side.

Line through midpoint parallel to second side

The line drawn from the midpoint of one side of a triangle, parallel to another side, bisects the third side.

Proportionality Theorem

A line drawn parallel to one side of a triangle divides the other two sides proportionally.

Similar Triangles (Equiangular)

If two triangles are equiangular, then the corresponding sides are in proportion and the triangles are similar.

Similar Triangles (Proportional Sides)

If the corresponding sides of two triangles are proportional, then the triangles are equiangular and consequently similar.

Equal Areas Theorem

If triangles (or parallelograms) are on the same base (or bases of equal length) and between the same parallel lines, then they have equal areas.

Tangent to a circle

The tangent is perpendicular to the radius or diameter of the circle at the point of contact.

Line from centre to midpoint of chord

The line drawn from the centre of a circle to the midpoint of a chord is perpendicular to the chord.

Line from centre perpendicular to chord

The line drawn from the centre of a circle perpendicular to a chord bisects the chord.

Angle at centre of a circle

The angle subtended by an arc at the centre is double the size of the angle subtended by the same arc at the circumference.

Angle in semi-circle

The angle subtended by the diameter at the circumference of the circle is $90^{\circ}$.

Angles in the same segment

Angles subtended by a chord of the circle, on the same side of the chord, are equal.

Concyclic points

If a line segment joining two points subtends equal angles at two points on the same side of the line segment, then the four points are concyclic.

Opposite angles of a cyclic quadrilateral

The opposite angles of a cyclic quadrilateral are supplementary.

Exterior angle of a cyclic quadrilateral

Equal to the interior opposite angle.

Tangents from common point

Two tangents drawn to a circle from the same point outside the circle are equal in length.

Tan-chord theorem

The angle between the tangent to a circle and the chord drawn from the point of contact is equal to the angle in the alternate segment.

Interior angles of a quadrilateral

The interior angles add up to $360^{\circ}$.

Parallelogram

A quadrilateral where opposite sides are parallel, opposite sides are equal in length, opposite angles are equal, and diagonals bisect each other.

Rhombus

A parallelogram where all four sides are equal, diagonals bisect at right angles, and diagonals bisect the interior angles.

Kite

A quadrilateral where diagonals intersect at right-angles, one diagonal bisects the other, and one diagonal bisects the opposite angles.