Which Vector Proofs do we actually need to know?

[chickenpop]

I'm a bit paranoid that I'll miss something

[TrueTears]

I doubt they'd put a really tricky one, but who knows they might, there are no "set" vector proofs which you have to memorise or whatever, what I suggest you do is remember the properties of the common shapes; squares, triangles, parallelograms etc. Knowing the specific properties for each of these shapes will tell you what you NEED to prove if you get a vector proof question

[98.40_for_sure]

Mr. tears...
is proving one right angle sufficient for proving a rectangle or square?

[jto1292]

I reckon you have to prove diagonals bisect for Square and Rect... It depends on actual question

[tram]

Mr. tears...
is proving one right angle sufficient for proving a rectangle or square?

I'm not tt but not, not JUST by it's self. If you can prove that there are two parallel sets of side AND that one od the angles is a right angle then yes that is sufficient. If you can also prove that all sies are of equal length, then it is a square.

I'm trying to think of a list of useful geometric properties.

- The diagonals in a rhombus are perpendicuar bisectors of each other
- The mid points of any quadlateral form a paralleogram
- A triangle subtended from the diameter of a circles is a right angled triangle

Hmmmmm geometery is not one of my strong points.... Any care to add what other properties are important to know?

[tram]

I reckon you have to prove diagonals bisect for Square and Rect... It depends on actual question

Diagonals only bisent each other in a rhombus, you need further evidence to prove it is a square and perpendicular bisectors are not related to rectangles

[98.40_for_sure]

It was this question from 08 vcaa exam 1 i think. The assessor report says this:

This was a straightforward question but many students did not recognise what additional property would lead to a
parallelogram being a rectangle. Many wasted time showing that the opposite pairs of sides had equal length or were
parallel. Some students tried to show that all four angles were right angles, or that all four angles were right angles and
opposite pairs of sides had equal length. A few students correctly showed an adjacent pair of sides were at right angles,
but then wasted time showing that adjacent sides were unequal in length, not realising that a square is a type of
rectangle. Students could also have shown that diagonals have equal length.

[Martoman]

Though i'm not a man crying, to answer your question, not necessarily. The other sides could have different lengths and angles.

It was this question from 08 vcaa exam 1 i think. The assessor report says this:

This was a straightforward question but many students did not recognise what additional property would lead to a
parallelogram being a rectangle. Many wasted time showing that the opposite pairs of sides had equal length or were
parallel. Some students tried to show that all four angles were right angles, or that all four angles were right angles and
opposite pairs of sides had equal length. A few students correctly showed an adjacent pair of sides were at right angles,
but then wasted time showing that adjacent sides were unequal in length, not realising that a square is a type of
rectangle. Students could also have shown that diagonals have equal length.

All you had to do for that one is show that one side had a right angle. That meant the oppoiste angle must be as well. With 2 right angles and two sides opposite each other the same, the other two angles must be right angles.

[98.40_for_sure]

Though i'm not a man crying, to answer your question, not necessarily. The other sides could have different lengths and angles.

I feel ya, it's just the assessor report leaves me discontent since they didn't make it clear what they actually want us to do with it.

[TrueTears]

http://vcenotes.com/forum/index.php/topic,17229.msg176466.html#msg176466

this is what I posted long time ago.

those are the definitions which DEFINE the shapes, prove them and you have proved the shape.

[itolduso]

how do you prove the altitudes of any triangle are concurrent?

[tram]

http://vcenotes.com/forum/index.php/topic,17229.msg176466.html#msg176466

this is what I posted long time ago.

those are the definitions which DEFINE the shapes, prove them and you have proved the shape.

cheers TT

[kyzoo]

All the proofs are the same? I dunno, it's jsut all right angles, shapes, and the occasional application of linaer independence

[tram]

All the proofs are the same? I dunno, it's jsut all right angles, shapes, and the occasional application of linaer independence

hmmmm vector proffs while aren;t conceptually hard are one of my weak areas.... i can do albedraic proofs (e.g. the trig proofs we often get) but the whole spacial thing just messes with my head.... i just don't see the thigns i need to....

[TrueTears]

lollll, vector proofs in year 12 are just geometry formalised

and yes geometry definitely aint my fave area of maths