Nested Triangles

Part of the Triangles section of Coddy's Geometry journey. Lesson 60 of 71.

Draw a line parallel to the base of a triangle. It cuts off a smaller triangle at the top. The two triangles are similar. They share the angle at the apex, and the parallel line makes the two base angles equal.

Be careful with the sides. The side of the large triangle runs from the apex all the way down to the base. So it is the small triangle's side plus the extra part below the cut.

$A triangle with a line parallel to its base cutting off a smaller triangle at the top: the upper part of the left side is 3, the lower part x, the small base 6 and the large base 10$

The side of the large triangle is 3 + x, from the apex to the base

In the figure, the upper part of the side is 3 and the lower part is x, so the whole side is x + 3. It matches the small triangle's side, which is 3. The large base, 10, matches the small base, 6. Write the proportion and solve it:

(x + 3)/3 = 10/6

x + 3 = 5

x = 2

Do not match the lower part x against the small side 3. The small triangle's side is only the upper part. The large triangle's side is the whole length from the apex to the base.

Challenge

A line parallel to the base cuts a triangle. The upper part of the left side is 4 and the lower part is x. The small base is 6 and the large base is 12.

$A triangle with a line parallel to its base cutting off a smaller triangle at the top: the upper part of the left side is 4, the lower part x, the small base 6 and the large base 12$

Find x.

Try it yourself

(x + 4)/4 = 12/6

Solve for x

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

Nested Triangles

All lessons in Triangles