Abbreviated circle geo reasoning allowed in hsc? (1 Viewer)

[jxballistic]

Hi guys,
at my school my teacher says were allowed to abbreviate our reasoning so for example instead of "angle between chord and tangent is equal to the angle in the alternate segment"we can write "alternate segment theorem", instead of "angle sum of straight line" we can write "st. ln." We're allowed to use a triangle symbol instead of writing triangle and that angle symbol sorta like " < " but the bottom like is horizontal.

In the hsc, are these allowed? Now since I've finished my 3u trial I've been thinking of changing to writing full reasoning. When I look through other school past paper solutions I see a mixture of full reasoning and abbreivated reasoning so I'm really confused.

 

[braintic]

Hi guys,
at my school my teacher says were allowed to abbreviate our reasoning so for example instead of "angle between chord and tangent is equal to the angle in the alternate segment"we can write "alternate segment theorem", instead of "angle sum of straight line" we can write "st. ln." We're allowed to use a triangle symbol instead of writing triangle and that angle symbol sorta like " < " but the bottom like is horizontal.

In the hsc, are these allowed? Now since I've finished my 3u trial I've been thinking of changing to writing full reasoning. When I look through other school past paper solutions I see a mixture of full reasoning and abbreivated reasoning so I'm really confused.

No-one is sure, they refuse to tell even teachers what is acceptable. But I'm pretty certain they will accept 'alternate segment theorem'. And I have my doubts about the acceptability of 'st.ln.' Of course you are allowed to use the angle symbol when naming an angle - I'm surprised that you aren't doing it already.

 

[asianese]

TBH they probably accept alternate segment theorem..

But...

If you want to be 10000% sure - JUST WRITE THE WHOLE THING!

There isn't a lot of circle geometry in any of the 3u or 4u papers (3-5 marks normally). It won't kill. And even if you scribble it half-legibly, this is still ok because the context is obvious.

 

[Drongoski]

Abbreviations should be allowed; but should be based on well -accepted ones. Maybe "st. ln." is not a good abbrev for "straight line".

 

[jxballistic]

I found this in the syllabus:
Definitions of circle, centre, radius, diameter, arc, sector, segment, chord,
tangent, concyclic points, cyclic quadrilateral, an angle subtended by an arc
or chord at the centre and at the circumference, and of an arc subtended by
an angle should be given.
Two circles touch if they have a common tangent at the point of contact.
2.8 Assumption: equal arcs on circles of equal radii subtend equal angles at the
centre, and conversely.
The following results should be discussed and proofs given. Reproduction
of memorised proofs will not be required.
Equal angles at the centre stand on equal chords. Converse.
The angle at the centre is twice the angle at the circumference subtended
by the same arc.
The tangent to a circle is perpendicular to the radius drawn to the point of
contact. Converse.
2.9 3 Unit students will be expected to be able to prove any of the following
results using properties obtained in 2.3 or 2.8.
The perpendicular from the centre of a circle to a chord bisects the chord.
The line from the centre of a circle to the midpoint of a chord is
perpendicular to the chord.
Equal chords in equal circles are equidistant from the centres.
Chords in a circle which are equidistant from the centre are equal.
Any three non-collinear points lie on a unique circle, whose centre is the
point of concurrency of the perpendicular bisectors of the intervals joining
the points.
Angles in the same segment are equal.
The angle in a semi-circle is a right angle.
Opposite angles of a cyclic quadrilateral are supplementary.
The exterior angle at a vertex of a cyclic quadrilateral equals the interior
opposite angle.
If the opposite angles in a quadrilateral are supplementary then the
quadrilateral is cyclic (also a test for four points to be concyclic).
If an interval subtends equal angles at two points on the same side of it
then the end points of the interval and the two points are concyclic.
The angle between a tangent and a chord through the point of contact is
equal to the angle in the alternate segment.
Tangents to a circle from an external point are equal.
The products of the intercepts of two intersecting chords are equal.
The square of the length of the tangent from an external point is equal to
the product of the intercepts of the secant passing through this point.
When circles touch, the line of centres passes through the point of contact.

Wow I never knew there were so many official converse theorems. I thought for converse proofs (like to prove 4 points are a cyclic quad) you could just state the original theorem with some extra reasoning... so for 2 angles standing on an interval I thought you could just say : since <a = <b and they are standing on the same interval, therefore ABCD is a cyclic quad (<'s standing on same arc in same segment are equal)

 

[nightweaver066]

http://community.boredofstudies.org/showthread.php?t=266895