The triangles ΔABC and ΔDEF are similar triangles by SAS theorem
What are similar triangles?
If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be ΔABC
The measure of side AB = 16
The measure of side AC = 36
And , the measure of ∠ABC = 105°
Let the first triangle be ΔDEF
The measure of side DE = 16
The measure of side DF = 36
And , the measure of ∠DEF = 105°
Now , the ratio of sides of the triangles is given by
AB / DE = AC / DF
4/16 = 9/36
1/4 = 1/4
So , corresponding sides of similar triangles are in the same ratio
And , the measure of angles = 105°
Therefore , by SAS , Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
Hence , they are similar triangles
To learn more about similar triangles click :
https://brainly.com/question/29378183
#SPJ5