Resolved: "Similar Triangles and Triginimetric Functions Use the figure..."

avissidep

Answered question

2021-02-06

Similar Triangles and Triginimetric Functions Use the figure below.
Explain why

△ A B C . △ A D E, and △ A F G

are similar triangles.

Answer & Explanation

Neelam Wainwright

Skilled2021-02-07Added 102 answers

Proof:
Consider the given triangle,

The $∠ A$ is part of all three triangles $△ A B C, △ A D E and △ A F G$ where, $∠ C = ∠ E = ∠ G = 90^{\circ}$ .
Since , sum of all angles of a triangle is $180^{\circ}$ so from the triangle ABC,
$∠ A + ∠ B + ∠ C = 180^{\circ}$
$∠ B = 180^{\circ} - ∠ A - ∠ C$
$= 180^{\circ} - ∠ A - 90^{\circ}$
$= 90^{\circ} - ∠ A$
In the triangle $△ A D E$ ,
$∠ A + ∠ D + ∠ E = 180^{\circ}$
$∠ D = 180^{\circ} - ∠ A - ∠ E$
$= 180^{\circ} - ∠ A - 90^{\circ}$
$= 90^{\circ} - ∠ A$
Similarly, from triangle AFG the angle $∠ F = 90^{\circ} — Z A$ .
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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