Find the Side Ratio: Comparing Triangles ABC and MNA in Geometric Analysis

Question

What is the ratio between the sides of the triangles ΔABC and ΔMNA?

00:00 Find the similarity ratio

00:03 Equal angles according to given data

00:07 The triangles share the same vertex angle

00:15 Similar triangles by AA

00:24 Let's find the similarity ratio

00:30 Similarity ratio is always the side opposite to the equal angle

00:41 We'll substitute appropriate values according to the given data and solve for the ratio

00:49 And this is the solution to the question

From the data in the drawing, it seems that angle M is equal to angle B

Also, angle A is an angle shared by both triangles ABC and AMN

That is, triangles ABC and AMN are similar respectively according to the angle-angle theorem.

According to the letters, the sides that are equal to each other are:

$\frac{AB}{AM}=\frac{BC}{MN}=\frac{AC}{AN}$

Now we can calculate the ratio between the sides of the given triangles:

$MN=3,BC=6$ $\frac{6}{3}=2$

$\frac{BC}{MN}=2$