Algebra, Geometry and Other Math: Geometry and Measurement
Angles, parallel lines, triangles and the Pythagorean theorem, plus perimeter, area, circles, volume, surface area and the units that belong to each.
11 topics · 50 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Angles, Lines and How They Are Measured
- How it worksHow does one full turn split into 360 degrees, and where do 90 and 180 land on it?
- Worked exampleFind the missing angle when two angles sitting on a straight line are 47 degrees and x.
- Worked exampleFind all four angles made where two straight lines cross if one of them is 55 degrees.
- Common mistakeWhy doesn't drawing the arms of an angle longer make the angle itself any bigger?
- Going furtherWhat happens to the four angles at a crossing as one of the lines rotates toward the other?
Your turneasy1 of 3
Two angles sit side by side on a straight line. One measures 117 degrees and the other measures x. Find x.Parallel and Perpendicular Lines
- How it worksHow does perpendicular mean exactly 90 degrees, and how do you spot it inside a shape?
- Worked exampleFind how many pairs of parallel sides a rectangle, a trapezoid and a triangle each have.
- Going furtherWhat happens to the gap between two parallel lines as you travel along them?
Your turnmedium1 of 3
A rectangle measures 15 cm by 11 cm. How many pairs of parallel sides does it have, and how does a trapezoid compare?Parallel Lines Cut by a Transversal
- How it worksHow does dragging one angle in a transversal picture move every angle equal to it at once?
- How it worksHow do corresponding, alternate and co-interior angles get their names from where they sit?
- Worked exampleFind all eight angles when a line crosses two parallel lines and one angle is 62 degrees.
- Worked exampleFind x when two co-interior angles between parallel lines measure 3x and 2x degrees.
- Going furtherWhat breaks in the angle rules when the two lines being crossed are not parallel?
Your turnhard1 of 3
A straight line crosses two parallel lines, and one of the eight angles measures 112 degrees. Find the co-interior angle that pairs with it.Triangle Angle Sum
- How it worksHow does tearing off three triangle corners and fitting them together make 180 degrees?
- Worked exampleFind the third angle of a triangle whose other two measure 43 and 78 degrees.
- Worked exampleFind the three angles of a triangle when they sit in the ratio 1 to 2 to 3.
- Going furtherWhat happens to the angle sum when you move from a triangle to a four-sided shape?
- Common mistakeWhy doesn't a hugely drawn triangle have a bigger angle sum than a tiny one?
Your turneasy1 of 3
A triangle has angles of 63 degrees and 71 degrees. Find the third angle.Right, Isosceles and Equilateral Triangles
- How it worksHow does folding an isosceles triangle down its middle prove the base angles match?
- How it worksHow do three equal sides force every angle of an equilateral triangle to be 60 degrees?
- Worked exampleFind the base angles of an isosceles triangle whose top angle is 40 degrees.
- Common mistakeWhy isn't every triangle with a 90 degree angle also an isosceles triangle?
- Worked exampleFind the two acute angles of a right triangle when one of them measures 27 degrees.
Your turneasy1 of 3
An isosceles triangle has a top angle of 104 degrees. Find one of its base angles. Round to two decimal places.The Pythagorean Theorem
- How it worksHow does pouring two small squares into the big one prove a squared plus b squared is c squared?
- How it worksHow do you work out which side is c before you start plugging any numbers in?
- Worked exampleFind the hypotenuse of a right triangle whose legs measure 6 and 8.
- Worked exampleFind the missing leg of a right triangle with a hypotenuse of 13 and one leg of 5.
- Going furtherWhat happens to the hypotenuse when both legs of a right triangle are doubled?
Your turneasy1 of 3
A right triangle has legs of 11 and 13. Find the hypotenuse. Round to two decimal places.Perimeter and Area of a Polygon
- How it worksHow does area count the unit squares tiling a shape while perimeter counts the fence around it?
- How it worksHow does cutting a parallelogram and sliding the piece turn it into a rectangle of equal area?
- Worked exampleFind the area and the perimeter of a rectangle 12 cm long and 7 cm wide.
- Worked exampleFind the area of a triangle with base 10 and height 6, and show where the half comes from.
- Worked exampleFind the area of an L-shaped room by splitting it into a 10 by 4 and a 6 by 3 rectangle.
Your turneasy1 of 3
A rectangle is 17 cm long and 11 cm wide. Find its area in square centimetres.Area and Circumference of a Circle
- How it worksHow does unrolling a circle into a straight segment show that circumference is 2 π r?
- How it worksHow does slicing a circle into wedges and interlocking them build a rectangle of area π r squared?
- Worked exampleFind the circumference and the area of a circle of radius 5, leaving π in the answer.
- Common mistakeWhy doesn't doubling a circle's radius simply double the area inside it?
- Worked exampleFind the radius of a circle whose circumference measures 18 π.
Your turneasy1 of 3
A circle has a radius of 13. Find its circumference. Round to two decimal places.Volume of a Cube, Cylinder and Box
- How it worksHow does filling a box layer by layer with unit cubes build the length times width times height rule?
- How it worksHow does a cylinder stack identical circles the way a box stacks flat rectangles?
- Worked exampleFind the volume of a box measuring 8 cm by 5 cm by 3 cm.
- Worked exampleFind the edge length of a cube whose volume is 64 cubic inches.
- Worked exampleFind the volume of a cylinder of radius 3 and height 10, leaving π in the answer.
Your turneasy1 of 3
A box measures 11 cm by 8 cm by 9 cm. Find its volume in cubic centimetres.Surface Area and Nets
- How it worksHow does unfolding a box into a flat net turn surface area into six rectangles you can add?
- Worked exampleFind the surface area of a cube with an edge of 5.
- Worked exampleFind the surface area of a box measuring 4 by 3 by 2.
- Going furtherWhat happens to a cube's surface area and to its volume when every edge is doubled?
Your turneasy1 of 3
A cube has an edge of 12. Find its surface area.Units of Measure and Converting Them
- How it worksHow do you decide whether a unit conversion should make the number bigger or smaller?
- Worked exampleFind how many square feet fit inside one square yard, and why the answer is not 3.
- Worked exampleFind how many minutes are in 2.5 hours and how many seconds are in 3 minutes.
Your turnmedium1 of 3
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