If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Course: High school geometry>Unit 4

Lesson 6: Proving relationships using similarity

Proof: Parallel lines divide triangle sides proportionally

Prove that a line parallel to one triangle side divides other sides proportionately. Created by Sal Khan.

Want to join the conversation?

• At , why did Sal put angle 2 and angle 4 in double arcs instead of single arcs?
• It’s just a way of expressing the angles are congruent. If the single arcs are already being used, the double arcs are the thing you would use next - but it dosen’t really matter
• Around in the video, I don't understand how Sal gets the EC and DB in the fractions.
• He starts from AE*BD=AD*EC. As he states, he divides both sides by EC first to give AE*DB/EC=AD*EC/EC, they cancel on the right, then he does the same thing by dividing by DB which cancels on the left to get the fractions.
• I just wanted to know why he continued the proof after saying that both triangles were similar since if they are similar then doesn't that mean that all 3 angles of 1 triangle each have a corresponding and equivalent second angle and the same thing with the sides except that they are propionate and not equivalent?
• If you state that N lines are of equal length, by the number of slashes you put in them. And for angles you add extra rings/slashes. (hypothetically) Is there a generally accepted way to visually state that line 'AB' of triangle ABC is proportionate to line 'XY' of triangle XYZ? It would really help me with writing notes.
• I don't know of any common way of noting it on a diagram, but if AB is proportional to XY, you could use a symbol used for proportionality: "∝". AB is proportional to XY would look like: AB ∝ XY.
• Isn't this also known as the basic proportionality theorem ?
• What does "leveraging" a triangle mean?
(1 vote)
• To leverage the diagram just means to make use of it. Studying the diagram may be helpful to solving the problem.
(1 vote)
• is this the thales theory?
(1 vote)
• No, Thales theorem says that if you inscribe a triangle in a circle, and one if its sides is a diameter of the circle, then the angle opposite that side is right.
(1 vote)
• When you insert the numbers given into the proof..One side is 1/3 while the other is 1/4 ?
(1 vote)
• The numbers shown in the videos are representing the angles, not the side measurements.
(1 vote)
• I cant make heads or toes what he means.