Write the triangle similarity statement and the reason for why the triangles \triangle XYZ\sim \triangle ? By: ? are similar.

Ernstfalld 2021-08-11 Answered
Write the triangle similarity statement and the reason for why the triangles are similar.
image
\(\displaystyle\triangle{X}{Y}{Z}\sim\triangle?{B}{y}:?\)

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Expert Answer

lamusesamuset
Answered 2021-08-12 Author has 17890 answers
Step 1
Taking \(\displaystyle\triangle{X}{Y}{Z}\)
\(\displaystyle\angle{X}={45}^{{\circ}},\angle{Y}={85}^{{\circ}}\)
Now,
Since sum of interior angle of triangle is \(\displaystyle{180}^{{\circ}}\)
\(\displaystyle\Rightarrow\angle{X}+\angle{Y}+\angle{Z}={180}^{{\circ}}\)
\(\displaystyle{45}^{{\circ}}+{85}^{{\circ}}+\angle{Z}={180}^{{\circ}}\)
\(\displaystyle\angle{Z}={180}^{{\circ}}-{130}^{{\circ}}\)
\(\displaystyle\angle{Z}={50}^{{\circ}}\)
Step 2
Taking \(\displaystyle\triangle{W}{Y}{U}\)
\(\displaystyle\angle{W}={50}^{{\circ}},\angle{Y}={85}^{{\circ}}\)
Now,
Since sum of interior angle of triangle is \(\displaystyle{180}^{{\circ}}\)
\(\displaystyle\Rightarrow\angle{W}+\angle{Y}+\angle{U}={180}^{{\circ}}\)
\(\displaystyle{50}^{{\circ}}+{85}^{{\circ}}+\angle{U}={180}^{{\circ}}\)
\(\displaystyle\angle{U}={180}^{{\circ}}-{135}^{{\circ}}\)
\(\displaystyle\angle{U}={45}^{{\circ}}\)
Step 3
In \(\displaystyle\triangle{X}{Y}{Z}\ {\quad\text{and}\quad}\ \triangle{U}{Y}{W}\)
\(\displaystyle\angle{X}=\angle{U}={50}^{{\circ}}\)
\(\displaystyle\angle{Y}=\angle{Y}={85}^{{\circ}}\)
\(\displaystyle\angle{Z}=\angle{W}={45}^{{\circ}}\)
Therefore
\(\displaystyle\triangle{X}{Y}{Z}\sim\triangle{U}{Y}{W}\) By: AA similarity
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