Pass Check: Vectors
Vectors have magnitude and direction; add tip-to-tail and use ratios for line proofs.
Vector
A quantity with both size (magnitude) and direction, e.g. written as a column (x, y) or with a letter and arrow.
Magnitude
The size (length) of a vector, found using Pythagoras on its components.
Parallel vectors
Vectors that are scalar multiples of each other, e.g. b = 2a means b is parallel to a and twice as long.
Resultant vector
The single vector obtained by adding two or more vectors together.
Quick check
Mixed quiz
1. Which theorem states that the angle at the centre is twice the angle at the circumference subtended by the same arc?
2. In a circle, angle BAC=90° where BC is a chord (not necessarily the diameter) and A is on the circle. What can you conclude about BC?
3. A triangle is inscribed in a semicircle with the diameter as one side. What type of triangle is guaranteed regarding one of its angles?
4. Triangle ABC and triangle DEF have AB=DE, angle A=angle D, angle B=angle E. Which condition proves congruence?
5. Two triangles share a common angle and have two pairs of corresponding sides in the same ratio. What can you conclude, and by which reasoning?
6. Triangle ABC has a right angle at B. Triangle DEF has a right angle at E. AC=DF (hypotenuses equal) and AB=DE. Which condition proves congruence?
7. Two triangles have all three corresponding angles equal but different side lengths. Are they congruent or similar?
8. A right-angled triangle has opposite side 8 cm and adjacent side 10 cm. Find the angle, to 1 decimal place.