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The short version A quadrilateral is any closed, flat shape with four straight sides and four corners. The four angles always add up to 360 degrees, no matter how stretched or lopsided the shape looks. Squares, rectangles, rhombuses, parallelograms, trapezoids and kites are all quadrilaterals, and they sit in a family tree where the special…
The short version An isosceles triangle has two sides of equal length, called the legs, and a third side called the base. The two angles sitting on the base are always equal. That’s the base angles theorem, and it works in reverse too. If you know the top angle, each base angle is (180 minus…
The short version There are six types of triangles: three named by side length (equilateral, isosceles, scalene) and three named by angle (acute, right, obtuse). Every triangle gets one label from each group, so a full name looks like “right scalene” or “obtuse isosceles.” All three angles always add to 180 degrees, which means no…
The short version The division symbol ÷ is called an obelus. It means “divided by,” so 12 ÷ 3 reads “twelve divided by three.” There are four ways to write the same thing: ÷, a slash like 12/3, a fraction bar with 12 on top and 3 underneath, and the long division bracket. Order matters….
The short version Integers are the counting numbers, their negatives, and zero: …, -3, -2, -1, 0, 1, 2, 3, … No fractions and no decimal parts. 7, -40 and 0 are integers. 2.5 and 3/4 are not. A number written as a decimal or fraction can still be an integer if it equals a…
The short version Irrational numbers can’t be written as a fraction of two integers, and their decimals run forever without ever settling into a repeating pattern. The famous ones are π, e, and the square root of any number that isn’t a perfect square, like √2 and √7. A decimal that stops (0.75) or repeats…
The short version A pentagon is a closed shape with five straight sides, five vertices and five angles. The interior angles of any pentagon add up to 540 degrees, regular or not. In a regular one every side matches and every interior angle is 540 ÷ 5 = 108 degrees. Perimeter is just the five…
The short version Real numbers are every number that sits somewhere on the number line: all the rationals plus all the irrationals. That covers counting numbers, zero, negatives, fractions, decimals that stop, decimals that repeat, and decimals that never repeat, like π. The sets nest inside each other. Natural fits in whole, whole fits in…
The short version A frequency table lists each value or category in one column and how many times it showed up in another. Build one by listing the categories, tallying each item once, counting the tallies, then checking that the frequencies add up to the number of items you started with. A grouped frequency table…
The short version The coordinate plane is a grid made by two number lines crossing at right angles: the horizontal x-axis and the vertical y-axis. They meet at the origin, written (0, 0). Every point on the grid gets an ordered pair (x, y). Always move along the x-axis first, then up or down. Right…