Question
Determine if triangles with the following angles are similar.
Triangle
Triangle
Triangle
Triangle
Ask by Ray Li. in the United States
Nov 20,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The triangles are not similar.
Solution
To determine if two triangles are similar, we need to check if their corresponding angles are equal. If two triangles have two pairs of corresponding angles that are equal, then the triangles are similar.
Given:
Triangle
Triangle
Triangle
Triangle
Let’s compare the angles of the two triangles:
- Triangle
has angles of and . - Triangle
has angles of and .
Since the angles of the two triangles are not equal, the triangles are not similar.
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Simplify this solution Mind Expander
To determine if triangles are similar based on their angles, we first need to identify the third angle for each triangle.
For Triangle
- The sum of all angles in a triangle is
. - Given angles are
and .
Calculating the third angle:
So, the angles in Triangle
For Triangle
- Given angles are
and . We must convert into degrees: - There are
minutes in a degree, so .
Calculating the third angle:
So, the angles in Triangle
Now we compare the angles of both triangles:
- Triangle
: - Triangle
:
Since none of the corresponding angles are the same (even the angle measures do not match), Triangle
