Parallel lines and trapezia · Grade 9
In Parallel lines and trapezia (Grade 9) you practise 4 skills: When are two lines parallel? · Angles in a trapezium · Area and perimeter of a trapezium · Is it a trapezium? On a coordinate grid. Two lines crossed by a third line are parallel if a pair of corresponding angles is equal, or a pair of alternate angles is equal, or the two angles between the lines on the same side of the third line add up to 180°. This is the converse of the angle facts for parallel lines: there the lines were known to be parallel and you found the angles; here the angles tell you that the lines are parallel.
A trapezium is a quadrilateral with exactly one pair of parallel sides. The other two sides are its legs. The two angles at the same leg add up to 180°, because they lie between the parallel sides on the same side of the leg. In an isosceles trapezium the legs are equal and the base angles are equal. The area of a trapezium is the sum of the parallel sides times the height, divided by 2. The height is the distance between the parallel sides, at right angles to both. On a coordinate grid, two sides are parallel when their gradients are equal, or when both are vertical.
Tip: To check whether a quadrilateral is a trapezium, test both pairs of opposite sides: in a trapezium exactly one pair is parallel.
What you learn
When are two lines parallel?
For example: The picture shows two lines and a third line crossing them. Given ∢1 = 75°, ∢5 = 75° . Are the lines parallel?
- Yes
- No
Answer and solution
The answer: Yes
Angles 1 and 5 are corresponding angles, and they are equal. So the lines are parallel.
Angles in a trapezium
For example: In the trapezium ABCD the bases are parallel: AB ∥ DC . Given ∢A = 45° . Find ∢D .
Answer and solution
The answer: 135 °
At the leg AD : ∢D = 180° − 45° = 135°
Area and perimeter of a trapezium
For example: The parallel sides of the trapezium are 7 cm and 5 cm, and its height is 4 cm. What is its area?
Answer and solution
The answer: 24 cm²
(7 + 5) × 4 ÷ 2 = 24
Is it a trapezium? On a coordinate grid
For example:
The points are A(1, −6), B(5, −6), C(7, −1), D(−1, 0) . Is the quadrilateral ABCD a trapezium?- Yes
- No
Answer and solution
The answer: No
The gradient of AB is 0 ÷ 4 = 0 The gradient of DC is −1 ÷ 8 The gradient of AD is −6 ÷ 2 = −3 The gradient of BC is 5 ÷ 2 No pair of opposite sides is parallel, so the quadrilateral is not a trapezium.
Not on the site yet
Parts of this topic that are not built yet: Proving that a quadrilateral is a trapezium · The midpoint segment of a trapezium.
The exercises are made by rules and the answers are worked out in code, so there are new exercises every time. The topic follows the Israeli Ministry of Education's grade 9 maths curriculum (2026–27).