Lines and Angles (Including Construction of Angles)
ICSE Class 7 · Mathematics · Chapter 14
What this chapter covers
- Lines, rays and angles: the words you need
- Complementary and supplementary angles
- Adjacent angles and the linear pair
- Vertically opposite angles
- Parallel lines and a transversal: naming the angles
- Properties of parallel lines cut by a transversal
- Construction of angles
- Construction of a line parallel to a given line
Key definitions
Intersecting lines are two lines that meet at exactly one point.
Parallel lines are lines in the same flat surface that never meet, however far they are extended.
Complementary angles are two angles whose measures add up to 90°.
Supplementary angles are two angles whose measures add up to 180°.
Adjacent angles are two angles that have a common vertex and a common arm, and whose other arms lie on opposite sides of the common arm.
Vertically opposite angles are the two angles that lie opposite each other when two lines intersect, sharing the vertex but having no arm in common.
Interior angles are the angles that lie between the two lines cut by the transversal.
Exterior angles are the angles that lie outside the two lines.
Corresponding angles are a pair of angles in matching positions at the two points where the transversal cuts the lines.
Alternate interior angles are a pair of interior angles that lie on opposite sides of the transversal.
Alternate exterior angles are a pair of exterior angles that lie on opposite sides of the transversal.
Co-interior angles are a pair of interior angles that lie on the same side of the transversal.
Key points
- Complementary angles add up to 90°; supplementary angles add up to 180°.
- Adjacent angles share a vertex and an arm, and do not overlap.
- A linear pair is a pair of adjacent angles on a straight line; they add up to 180°.
- Angles round a point add up to 360°.
- Vertically opposite angles are formed by two intersecting lines and are always equal.
- A transversal cutting two lines forms eight angles: four interior and four exterior.
- When the lines are parallel, corresponding angles are equal, alternate angles are equal and co-interior angles add up to 180°.
- Equal corresponding angles, equal alternate angles, or co-interior angles adding to 180° show that two lines are parallel.
- With compasses you can copy an angle, construct 60° and 120°, and bisect an angle to get 30°, 90°, 45° and more.
- A line through a point parallel to a given line is drawn by copying an angle to make equal alternate or corresponding angles.