Properties of triangles, quadrilaterals and circles
Derive and illustrate properties of triangles, quadrilaterals, and circles using appropriate language, including interior angles, diagonals, symmetry, and relationships between side lengths
What a learner can do afterwards
- List and verify properties of a parallelogram (opposite sides parallel/equal, opposite angles equal, diagonals bisect each other)
- Explain why a square is a special case of both a rectangle and a rhombus
- Derive the relationship between the radius, diameter, and circumference of a circle
1 · Read
A parallelogram is a four-sided shape where both pairs of opposite sides are parallel. In a parallelogram, opposite sides are always equal in length, and opposite angles are always equal to each other. The two diagonals also do something special: they bisect each other, meaning each diagonal cuts the other exactly in half at the point where they cross.
Picture a parallelogram ABCD, where AB is opposite CD, and BC is opposite AD. If AB measures 6 cm, then CD also measures 6 cm, since opposite sides are equal. If angle A measures 70 degrees, then angle C, its opposite angle, also measures 70 degrees. Now draw both diagonals, AC and BD: they cross at one point, and that point splits each diagonal into two equal halves.
A rectangle is a parallelogram with four right angles. A rhombus is a parallelogram with four equal sides. A square fits both descriptions at once: it has four right angles, like a rectangle, and four equal sides, like a rhombus. That is why a square counts as a special case of both a rectangle and a rhombus, rather than being a separate shape on its own.
For any circle, the diameter is always twice the radius: d = 2r. The circumference, the distance around the circle, is always about 3.14 times the diameter, written as C = pi times d. That number, pi, is the same for every circle, no matter how big or small.
Parallelograms have equal opposite sides and angles with diagonals that bisect each other, a square is a rectangle and a rhombus at once, and a circle's circumference is always pi times its diameter.
2 · Watch
Take it off screen
Where it sits
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.