Intermediate II Geometry, Coordinate Geometry, and Measurement (5-6 new curriculum)

Question 1

reflection symmetry

Answer 1

2D: if there is a straight line over which the shape reflects and the two halves match exactly

3D: if there is a plane over which the shape reflects and the two halves match exactly

In a regular polygon, the number of sides equals the number of reflection symmetries.

The circle has infinitely many reflection symmetries.

Question 2

rotation symmetry

Answer 2

if it exactly overlaps itself one or more times within a rotation of less than 360 degrees around its centre point

In a regular polygon, the number of sides equals the number of rotation symmetries.

The circle has infinitely many rotation symmetries.

Question 3

order of rotation (order of rotation symmetry)

Answer 3

the number of times a shape coincides with itself within a rotation of 360 degrees around its centre point

Question 4

central symmetry

Answer 4

rotational symmetry by 180 degrees

the straight line that connects a point with its image in the central symmetry passes through the centre of rotation

Question 5

How can a symmetrical shape be mapped?

Answer 5

by any combination of reflections and rotations

Question 6

tessellation

Answer 6

the tiling of a plane with symmetrical shapes

Question 7

symmetry

Answer 7

a relationship within a shape that can be mapped exactly onto itself other through reflection or rotation

e.g.:
the two parts of the shape for example can be congruent to each other and thus make the full shape symmetrical

Question 8

congruent

Answer 8

two things that can be placed on top of one another without changing any lengths (maybe by using a rigid motion and then reflection at the end)

a relationship between two shapes of identical size and shape

congruence is not dependent on orientation or location of the shapes

Question 9

What are some units of area?

Answer 9

square centimetres (equivalent to the area of a square measuring 1 centimetre by 1 centimetre)
square metres
square kilometres

(many more exist but are not listed here)

exponent 2 on the unit

Question 10

Among all rectangles with the same area, the square has the (least/most) perimetre

Answer 10

least

Question 11

Can rectangles with the same area have different perimetres?

Answer 11

yes

Question 12

parallelogram

Answer 12

any quadrilateral with two pairs of parallel and equal sides

any side of the parallelogram can be interpreted as the base

the height of a parallelogram is the perpendicular distance from its base to its opposite side

Question 13

triangle area

Answer 13

half the area of the parallelogram with the same base and height

A = hb/2

Question 14

If two triangles have the same base and height, then what can we say about their areas?

Answer 14

the areas are also the same

Question 15

parallelogram area

Answer 15

the product of the perpendicular base and height

A = bh

Question 16

area of composite shapes

Answer 16

shapes made by combining shapes

area can be found by adding all the areas together

Question 17

units of volume

Answer 17

cubic centimetres (a cubic centimetre is one centimeter mutliplied by one centimetre multiplied by one centimetre)
cubic metres

exponent 3 on the unit

Question 18

volume of right rectangular prism

Answer 18

the product of the 2D base area and the perpendicular height of the prism

V = (A of base)(h)