# Given the 2 sets of figures below, are the pairs of triangles similar for both set a and set b? Why or why not? What is the similarity statement and the scale factor?

Nov 22, 2017

See explanation.

#### Explanation:

In example $A$ triangles are simolar.

The left triangle has angles of: $79$, $67$ and $34$ degrees.
The last angle can be calculated as: $180 - 79 - 67$

The right triangle has angles of $34$, $67$ and $79$ degrees, so the triangles are similar (angle-angle-angle property)

The scale can be calculated as:

$s = \frac{30}{45} = \frac{2}{3}$

So triangle $R L G$ is$\frac{2}{3}$ times smaller than $N P C$

In example $B$ the triangles are NOT similar.

If they were similar, they would have to have 3 pairs of equal angles. In these triangles there is only one pair of equal angles: $F = K$