Similar Triangles and Triginimetric Functions Use the figure below. Explain why /_ABC. /_ADE, and /_AFG are similar triangles.

avissidep 2021-02-06 Answered
Similar Triangles and Triginimetric Functions Use the figure below.
Explain why ABC.ADE,andAFG are similar triangles.
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Expert Answer

Neelam Wainwright
Answered 2021-02-07 Author has 102 answers

Proof:
Consider the given triangle,
image
The A is part of all three triangles ABC,ADEandAFG where, C=E=G=90.
Since , sum of all angles of a triangle is 180 so from the triangle ABC,
A+B+C=180
B=180AC
=180A90
=90A
In the triangle ADE,
A+D+E=180
D=180AE
=180A90
=90A
Similarly, from triangle AFG the angle F=90ZA.
Therefore, B=D=F.
Since two of the angles of the triangles are equal, the third angle is also equal.
Therefore, the triangles are similar due to AAA similarity criterion.

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