a What kind of a triangle is △ LMN? How about the triangle your are comparing △ LMN to?
B
b Notice that all sides have a length of a. What kind of triangle is this?
C
c Notice that all sides have a length of 2. What kind of triangle is this?
D
d Notice that all sides have a length of 5. What kind of triangle is this?
A
a Similar
B
b Similar
C
c Similar and congruent
D
d Similar
Practice makes perfect
a We see that △ LMN has three congruent sides, which means it is an equilateral triangle. Since all equilateral triangles are similar, the given triangle has to be equilateral as well in order for it to be similar. In addition to three congruent sides, an equilateral triangle also has three congruent angles, each of them 60^(∘).
We now know that the given triangle in Part A must be similar to △ LMN, as the triangles has three pairs of congruent angles.
b The given triangle has three sides with a length of a. This means it has three congruent sides and is therefore equilateral.
As argued in Part A, all equilateral triangles are similar. Therefore, this triangle is also similar to △ LMN.
c Let's consider the given triangle.
Just like in Part B, this triangle has three congruent sides which means it is an equilateral triangle. Therefore, this triangle is similar to △ LMN. Also, since the length of the sides are 2, the triangle is also congruent to △ LMN.
d Again, like in Part B and C this triangle has three congruent sides, which means it is an equilateral triangle.
Therefore, this triangle is also similar to △ LMN.
