Answered: "Proving Similarity in the figure DEFG is a..."

High School
Geometry
High school geometry
Similarity

beljuA

Answered question

2020-11-08

Proving Similarity in the figure DEFG is a square. Prove the following:
$△ A D G \sim △ F E B$
Given:
The given figure is,

Answer & Explanation

SabadisO

Skilled2020-11-09Added 108 answers

Approach:
If the first triangle is similar to the second triangle and second triangle is similar to the third triangle then, the first triangle is similar to the third triangle.
Calculation:
Its given that DEFG is a square.
Consider

△ G C F and △ F E B

∠ F E B = ∠ G C F

both are

90^{\circ}

.
And

G F ∣ ∣ A B, t h u s, ∠ C F G = ∠ F B E

as they are alternate angles.
Therefore,

△ G C F \sim △ F E B

by AA rule.
Since,

△ G C F \sim △ F E B and △ A D G \sim △ G C F, h e n c e, △ A D G \sim △ F E B

Conclusion:
Hence, it is proved that

△ A D G \sim △ F E B

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