The PDF file titled "Mathematics 9 DBE/2014 Examination Guidelines" provides a comprehensive guide to the examination guidelines for a Mathematics course at the 9th-grade level. The document is designed for educational use, specifically within the South African context, and offers a structured brea...
4. ACCEPTABLE REASONS: EUCLIDEAN GEOMETRY
In order to have some kind of uniformity, the use of the following shortened versions of the theorem
statements is encouraged.
4.1 ACCEPTABLE REASONS: EUCLIDEAN GEOMETRY (ENGLISH)
THEOREM STATEMENT ACCEPTABLE REASON(S)
LINES
The adjacent angles on a straight line are supplementary. ∠s on a str line
If the adjacent angles are supplementary, the outer arms of these adj ∠s supp
angles form a straight line.
The adjacent angles in a revolution add up to 360°. ∠s round a pt OR ∠s in a rev
Vertically opposite angles are equal. vert opp ∠s =
If AB || CD, then the alternate angles are equal. alt ∠s; AB || CD
If AB || CD, then the corresponding angles are equal. corresp ∠s; AB || CD
If AB || CD, then the co-interior angles are supplementary. co-int ∠s; AB || CD
If the alternate angles between two lines are equal, then the lines are alt ∠s =
parallel.
If the corresponding angles between two lines are equal, then the corresp ∠s =
lines are parallel.
If the cointerior angles between two lines are supplementary, then coint ∠s supp
the lines are parallel.
TRIANGLES
The interior angles of a triangle are supplementary. ∠ sum in ∆ OR sum of ∠s in ∆
OR Int ∠s ∆
The exterior angle of a triangle is equal to the sum of the interior ext ∠ of ∆
opposite angles.
The angles opposite the equal sides in an isosceles triangle are ∠s opp equal sides
equal.
The sides opposite the equal angles in an isosceles triangle are sides opp equal ∠s
equal.
In a right-angled triangle, the square of the hypotenuse is equal to Pythagoras OR
the sum of the squares of the other two sides. Theorem of Pythagoras
If the square of the longest side in a triangle is equal to the sum of Converse Pythagoras
the squares of the other two sides then the triangle is right-angled. OR
Converse Theorem of Pythagoras
If three sides of one triangle are respectively equal to three sides of SSS
another triangle, the triangles are congruent.
If two sides and an included angle of one triangle are respectively SAS OR S∠S
equal to two sides and an included angle of another triangle, the
triangles are congruent.
If two angles and one side of one triangle are respectively equal to AAS OR ∠∠S
two angles and the corresponding side in another triangle, the
triangles are congruent.
If in. two right angled triangles, the hypotenuse and one side of one RHS OR 90°HS
triangle are respectively equal to the hypotenuse and one side of the
other, the triangles are congruent
The line segment joining the midpoints of two sides of a triangle is Midpt Theorem
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