Shape Flashcards
(18 cards)
How does a negative scale factor work?
It has the same effect as positive, except it goes in the opposite direction. Lets say you enlarge shape OA (11) with a SF of -2. You would do OA(11) x -2=(-2-2)
How do column vectors work?
They tell you how far a shape is from the centre of enlargement. The top number is how far to the right, the bottom up.
How does a fractional scale factor work?
It makes the shape smaller. Say you enlarge a shape by 1/2 around 0,0, each point will be twice as close to the centre of enlargement.
What conditions are needed for a triangle to be congruent?
A congruent triangle is exactly the same size and shape.
1) SAS- two sides and the angle between them are equal
2) SSS- all 3 sides are the same length
3) ASA- two angles and the included side are equal
4) RHS- both are right angled, and one side and the hypotenuse are equal
How are shapes similar?
Shapes are similar if they have the same angles, and the sides have been enlarged by the same ratio. If you can prove either of these, then they are similar. The scale factor can be shown by finding corresponding lengths, and creating a fraction.
How do you find missing lengths?
You times the smaller length, by the enlarged scale-factor, to get the bigger length. To find a smaller length, you divide the big length by the scale factor.
How do you find the area or volume scale factor?
The area scale factor is normal squared. The volume is normal cubed. To find the area of a similar shape, you find the scale factor, then you square it, then you multiply the known area by the area scale factor.
How do you find a side using trig?
Find the correct part of SOHCAHTOA, using the side you know the length of, and the side you’re trying to find. Do that ratio then the angle you know, equal to x/the side you know. You need to get x by itself, so do the length times by SOHCAHTOA then the angle. The answer is the length.
What are the scale factor and the centre of enlargement?
A scale factor is how much bigger you make it. A centre of enlargement tells us from where it is being enlarged from
How do you find an angle using trig?
Identify the values you know, then choose the trig function. Substitute the values into the normal trig function.. Then do inverse function, followed by one length over the other, to get the angle.
How do you trig in an isosceles triangle?
Split it down the middle, to get two right angled triangles.
How are bearings measured?
They are always measured from north, in a clockwise direction, and they have three figures.
What are the nine circle theorems?
1) isosceles triangle if two sides are radii
2) angles subtended by an arc are equal
3) triangle in a semicircle is right angles
4) angle at the centre is twice angle at circumfrence
5) perpendicular bisector of chord through centre
6) cyclic quadrilateral opposite corners equal 180
7) angle between tangent and radius is 90
8) tangents from a point are equal
9) alternant segment angles are equal
Outline the arrow head theorem
When you have two or more raddii, the angle between the bigger part of them is double the angle where they meet up.
Outline the cyclic quadrilateral theorem
If a quadrilateral is in a circle with all four corners touching the sides, the opposite corners will equal 180*
Outline the alternate segment theorem
When a triangle is inside a circle, with each point touching the edge, and a tangent at one of the points, the angle from the tangent to the chord will be equal to the angle inside the triangle on the opposite side.
What is the area of a sector?
θ/360 x πr^2
What is the area of a segment?
(θ/360 x πr^2) - (1/2²sinθ)
Area of segment - area triangle
