Plane Geometry: Triangles and Quadrilaterals
Triangles and quadrilaterals are polygons whose side lengths and angles can be classified, constructed and measured.
Triangles
Triangles may be classified by sides as equilateral, isosceles or scalene, and by angles as acute, right-angled or obtuse. The interior angles of every triangle sum to 180°. A perpendicular height is drawn from a vertex to the opposite side, and a median joins a vertex to the midpoint of the opposite side.
Measures and construction
The perimeter of a triangle is a + b + c. Its area is 1/2 × base × perpendicular height. A triangle can be constructed when suitable side and angle information is given; use a ruler, compass and protractor carefully.
Quadrilaterals
A quadrilateral has four sides and its interior angles sum to 360°. A square has four equal sides and four right angles; a rectangle has equal opposite sides and four right angles; a parallelogram has equal opposite sides; a rhombus has four equal sides; and a trapezium has one pair of parallel sides.
Worked examples and practice
- A triangle with base 8 cm and height 5 cm has area 1/2 × 8 × 5 = 20 cm².
- If two triangle angles are 50° and 65°, the third is 180° − 115° = 65°.
- Find the perimeter of a 6 cm by 4 cm rectangle and the missing angle of a quadrilateral with other angles 80°, 90° and 110°.
