Question

These triangles ARE similar! Which reason proves it?

Answer 1

Answer:

SAS

Step-by-step explanation:

From the image attached below, in triangle ABC, AB = 15, AC = 20 while in triangle ADE, AD = 12 and AE = 16

Two triangles are said to be similar if they have the same shape, that is either their corresponding angles are the same or their corresponding sides are proportional.

For both triangle ABC and triangle ADE, they have the same angle which is ∠A. Also:

$\frac{AD}{AB}=\frac{12}{15}=\frac{4}{5}$

$\frac{AE}{AC}=\frac{16}{20}=\frac{4}{5}$

Since two sides of triangle ABC are in the same proportion as two sides of triangle ADE and they have the same angle, therefore they are similar based on the SAS  (side-angle-side) similarity