Triangle Similarity Ratio: Finding the Scale Factor Between Two Intersecting Triangles

Question

What is the ratio of similarity between the triangles shown in the diagram below?

00:05 Let's find out which triangles are similar and what their similarity ratio is.

00:11 First, look for equal angles given in the problem. Remember, equal angles help us identify similar triangles.

00:18 Also, spot any perpendicular lines in the data. This is important for our comparison.

00:24 If two angles are equal between the triangles, then we know the third angle must be equal too!

00:33 This means the triangles are similar by the Angle-Angle, or AA, rule.

00:44 Next, remember that corresponding sides are opposite to those equal angles.

00:54 And that's how we find our similarity ratio, by comparing those sides.

01:01 Great job! That's the solution to the question.

From the drawing it appears that angle E equals angle A

Since angle D equals 90 degrees, its adjacent angle also equals 90 degrees.

In other words, angle D1 equals angle D2 and both equal 90 degrees.

Since we have two pairs of equal angles, the triangles are similar.

Also angle B equals angle C

Now let's write the similar triangles according to their corresponding angle letters:

$ABC=ECD$

Let's write the ratio of sides according to the corresponding letters of the similar triangles:

$\frac{AB}{EC}=\frac{AD}{ED}=\frac{BD}{CD}$

$\frac{AB}{EC}=\frac{AD}{ED}=\frac{BD}{CD}$