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?

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Answer 1 · 2017-11-22T22:41:12

See 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:

$s=30/45=2/3$

So triangle $RLG$ is $2/3$ times smaller than $NPC$

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: $F=K$