Similar Triangles Proof: Analyzing ΔACB∼ΔBED with 30° and 60° Angles

Question

$ΔACB∼ΔBED$

Choose the correct answer.

00:00 Choose the correct answer

00:03 Find the side opposite to the 30-degree angle in both triangles

00:14 Use the same method for the 90-degree angle in both triangles

00:23 And the same for the 60-degree angle in both triangles

00:33 The similarity ratio is always the side opposite to the equal angle

00:53 Let's use the transition rule

00:57 And this is the solution to the question

First, let's look at angles C and E, which are equal to 30 degrees.

Angle C is opposite side AB and angle E is opposite side BD.

$\frac{AB}{DB}$

Now let's look at angle B, which is equal to 90 degrees in both triangles.

In triangle ABC the opposite side is AC and in triangle EBD the opposite side is ED.

$\frac{AC}{ED}$

Let's look at angles A and D, which are equal to 60 degrees.

Angle A is the opposite side of CB, angle D is the opposite side of EB

$\frac{CB}{EB}$

Therefore, from this it can be deduced that:

$\frac{AB}{BD}=\frac{AC}{ED}$

And also:

$\frac{CB}{ED}=\frac{AB}{BD}$

Answers a + b are correct.