Math Test Friyay

Quadrilateral

A 2D shape with 4 sides

Square

4 equal sides, 4 right angles, and opposite sides parallel

Rectangle

4 right angles; opposite sides are equal and parallel

Rhombus

4 equal sides; opposite angles are equal and opposite sides are parallel

Parallelogram

Opposite sides are equal and parallel; opposite angles are equal

Trapezium

A quadrilateral with one pair of parallel sides

Kite

A quadrilateral with two pairs of adjacent equal sides

Square → Rectangle → Parallelogram

A square is always a rectangle and a rectangle is always a parallelogram, but the reverse is not necessarily true

Congruent triangles

Triangles with exactly the same size and shape

Congruence: SSS

Side-Side-Side: all 3 corresponding sides are equal

Congruence: SAS

Side-Angle-Side: 2 corresponding sides and the included angle are equal

Congruence: ASA

Angle-Side-Angle: 2 corresponding angles and the included side are equal

Congruence: AAS

Angle-Angle-Side: 2 corresponding angles and a corresponding side are equal

Congruence: RHS

Right angle-Hypotenuse-Side: both triangles have a right angle, equal hypotenuses and one equal corresponding side

Similarity

Two triangles have the same shape but can be different sizes

Similar triangles

Same corresponding angles and proportional corresponding sides

Similarity: AAA

All corresponding angles are equal

Similarity: SSS

All corresponding sides are in the same ratio

Similarity: SAS

Two corresponding sides are in the same ratio and the included angles are equal

Congruent vs similar

Congruent = same size AND shape; similar = same shape but not necessarily same size

Scale factor

The number you multiply a length by to get the corresponding length in the other similar shape

Scale factor formula

New length ÷ original length

Scale factor example

If 6 cm becomes 9 cm: 9 ÷ 6 = 1.5

Using a scale factor

Multiply the original length by the scale factor

Working backwards with a scale factor

Divide the new length by the scale factor

Proving triangles are similar

Show that the triangles satisfy AAA, SSS or SAS, then state the similarity test

Corresponding sides

Sides that occupy the same position in similar or congruent triangles

Perimeter

The total distance around the outside of a shape

Perimeter rule

Add every outside side; do not count internal lines

Composite perimeter

Add only the lengths around the OUTSIDE boundary of the entire shape

Composite perimeter trick

Trace around the outside edge with your finger and count only those sides

Pythagoras' theorem

In a right-angled triangle, a² + b² = c²

Hypotenuse

The longest side of a right-angled triangle, opposite the right angle

Finding the hypotenuse

Add the squares of the two shorter sides, then square root

Finding a shorter side

Subtract the square of the known shorter side from the square of the hypotenuse, then square root

Pythagoras memory trick

Hypotenuse = ADD; shorter side = SUBTRACT

Pythagoras word problem clues

Look for a right angle and words like ladder, diagonal, across, or shortest distance

Circumference

The distance around a circle

Circumference using diameter

C = πd

Circumference using radius

C = 2πr

Diameter

The distance across a circle through its centre; diameter = 2 × radius

Radius

The distance from the centre of a circle to its edge

Ferris wheel: one rotation

One complete rotation = one circumference

Distance for multiple rotations

Circumference × number of rotations

Finding number of rotations

Total distance ÷ circumference

Finding diameter from circumference

Divide circumference by π

Perimeter vs circumference

Perimeter is used for polygons/shapes; circumference is the distance around a circle

Pythagoras vs perimeter

Pythagoras finds a missing length; perimeter adds the outside lengths

Pythagoras vs circumference

Pythagoras is for right-angled triangles; circumference is for circles

How to recognise perimeter

Question asks how far around a shape or how much fencing is needed

How to recognise circumference

Question asks distance around a circle, wheel or circular track

How to recognise Pythagoras

Question involves a right-angled triangle and a missing side

How to recognise similarity

Look for triangles with the same shape, proportional sides or equal corresponding angles

How to recognise congruence

Look for triangles that must be exactly the same size and shape

AAS warning

AAS can prove CONGRUENCE; it is not automatically a similarity test

True or false: All squares are rectangles

TRUE

True or false: A trapezium is a parallelogram

FALSE

True or false: A rhombus can be a kite

TRUE

True or false: Some parallelograms are squares

TRUE

True or false: Every quadrilateral is a parallelogram

FALSE

True or false: All rhombuses are squares

FALSE

Most important congruence memory

SSS, SAS, ASA, AAS, RHS

Most important similarity memory

AAA, SSS, SAS

Most important Pythagoras memory

H = ADD; SHORT = SUBTRACT

Most important circle memory

C = πd or C = 2πr

Most important scale factor memory

NEW ÷ ORIGINAL

Most important perimeter memory

OUTSIDE ONLY