Properties of perpendicular lines 1. They intersect, or meet each - PowerPoint PPT Presentation

D AY 3 – D EFINITION OF PERPENDICULAR LINES

I NTRODUCTION In real life we see objects meeting or intersecting at right angles. For example, the sides of rectangular and square floor tile meet at right angles, motor joints of buildings are designed to be either vertical or horizontal thus meeting at right angles with each other. In this lesson we are going to learn what perpendicular lines are and some of their basic properties.

V OCABULARY Intersecting lines These are two or more lines that cross each other at point(s) called the point(s) of intersection . P S O Q R 𝑄𝑅 and 𝑆𝑇 intersect and point O. Point O is common to both lines.

P ERPENDICULAR LINES Two rays, line segments or lines, are perpendicular to each other if they intersect or meet at right angles. S P R Q 𝑄𝑅 is perpendicular to 𝑆𝑇 , written as 𝑄𝑅 ⊥ 𝑆𝑇 .

Properties of perpendicular lines 1. They intersect, or meet each other, at 90° . 2. If two lines intersect at 90° they form four right angles at the point of intersection.

Example 1 Identify whether the pairs of intersecting lines below are perpendicular or not. (a)

(b)

(c)

(d)

Solution (a) Not perpendicular because they do not intersect at 90°. (b) Perpendicular because they intersect at 90° . (c) Perpendicular (d) Not perpendicular

Example 2 Considering the cube below identify any four pairs of perpendicular line segments. E F G H D C A B

Solution These are among the perpendicular line segments in the cube: 𝐵𝐶 and 𝐶𝐷 , 𝐵𝐶 and 𝐵𝐸, 𝐵𝐶 and 𝐵𝐼, 𝐵𝐶 and 𝐶𝐻 , 𝐶𝐷 and 𝐷𝐸, 𝐶𝐷and 𝐶𝐻 , 𝐶𝐷and 𝐷𝐺 , 𝐷𝐸 and 𝐵𝐸, 𝐷𝐸and 𝐷𝐺 , 𝐷𝐸and 𝐸𝐹.

H OMEWORK Identify pairs of perpendicular lines or segments in the figure below. A D C F E B G

A NSWERS TO HOMEWORK 𝐵𝐷 and 𝐵𝐺 , 𝐵𝐸 and 𝐸𝐶, 𝐸𝐶 and 𝐺𝐹, 𝐹𝐻 and 𝐺𝐹

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