Trapezium
FoundationOne pair of parallel sides.
- A trapezium has exactly 1 parallel pair
- Parallel sides are the bases; slanted sides are legs
- Height is the perpendicular distance between bases
1Summary 重點摘要
One pair of parallel sides.
2Vocabulary cards Vocabulary
A quadrilateral with exactly one pair of parallel sides.
The top parallel side, usually shorter.
The bottom parallel side, usually longer.
The two non-parallel sides on the left and right.
The perpendicular distance between the two bases.
A trapezium whose legs are equal; it looks left-right symmetric.
The trapezium's only pair: upper base parallel to lower base.
Rectangles, squares and parallelograms have two parallel pairs; a trapezium has just one.
3Step by step Steps
- Part 1: Defining the trapeziumDraw a 6 cm line as the lower base, then another 3 cm line above it as the upper base, keeping the two lines parallel, and join the ends with two slanting sides. This figure has exactly one parallel pair — the bases — while the two legs are not parallel: it is a trapezium.
- Part 2: Naming the partsIn a trapezium the top parallel side is the upper base, say 3 cm; the bottom one is the lower base, say 6 cm; the two slanting sides are the legs; and the vertical gap between the bases is the height. Learn these four names, because they return in the lessons on area.
- Part 3: Trapezium versus parallelogramA parallelogram has two parallel pairs; a trapezium has only one — that is the main difference. Imagine shortening one side of a parallelogram: two parallel pairs become one, and the shape turns into a trapezium. Count the parallel pairs to tell them apart.
- Part 4: The isosceles trapeziumA trapezium whose two legs are equal in length is called an isosceles trapezium, for example with both legs 4 cm. It is symmetric left to right: fold it along the middle and the two halves cover each other exactly. Bucket sides and lampshade sides often have this shape.
- Part 5: How to measure the heightTo measure the height, place one right-angle edge of a set square along the lower base; the other right-angle edge just touches the upper base, and that perpendicular distance is the height. Wherever you measure it, the height is the same, because the two bases are parallel.
- Part 6: Trapeziums around usThe side of a stair, lampshades, bucket sides, the cross-section of a dam, and the side panels of some handbags are all trapeziums. The test comes down to one sentence: a quadrilateral with four sides and exactly one parallel pair is a trapezium.
4Diagrams Diagrams
5Worked example Example
Example: a quadrilateral has an upper base of 4 cm, a lower base of 8 cm, legs of 5 cm each, and the two bases are parallel. (1) What shape is it? (2) Is it an isosceles trapezium? (3) How many parallel pairs does it have?
- (1) Count parallel sides: only the upper and lower bases are parallel, so it is a trapezium.
- (2) Compare the legs: both are 5 cm, equal in length, so it is isosceles.
- (3) Only the bases form 1 parallel pair, because the two legs are not parallel.
- Cross-check: a parallelogram needs two parallel pairs, and this figure does not qualify.
- Answer: Answer: (1) it is a trapezium; (2) yes, an isosceles one; (3) exactly 1 parallel pair. To judge a trapezium, count the parallel pairs first and then compare the legs; unlike a parallelogram, a trapezium always has only one pair.
6Common mistakes Mistakes
7Quick check Quick check
Q1How many parallel pairs does a trapezium have?
Q2What are the parallel sides called?
Q3A trapezium with equal legs is called?
Q4How is a trapezium's height measured?
Q5Shorten one side of a parallelogram — what shape appears?
8Recap Recap
- A trapezium has exactly 1 parallel pair
- Parallel sides are the bases; slanted sides are legs
- Height is the perpendicular distance between bases
- Equal legs make an isosceles trapezium, left-right symmetric
- Versus parallelogram: one pair versus two