Get the solution to "Determine if the figures are similar. If they..."

kuCAu

Answered question

2021-08-09

Determine if the figures are similar. If they are similar by what similarity theorem?

a)AA
b)SAS
c)SSS
d)Not Similar

Delorenzoz

Skilled2021-08-10Added 91 answers

Step 1
The two triangles are given which is

△ A C B and △ D F E

.
In

△ D F E

,
Sum of all the angles of the triangle is

180^{\circ}

∠ F + ∠ E + ∠ D = 180^{\circ}

79^{\circ} + 41^{\circ} + ∠ D = 180^{\circ}

∠ D = 180^{\circ} - (79^{\circ} + 41^{\circ})

= 180^{\circ} - 120^{\circ}

= 60^{\circ}

△ A C B and △ D F E

∠ D F E = ∠ A C B

(Corresponding angles are equal)
As

∠ D F E = ∠ A C B = 79^{\circ}

.
Step 2
Similarly,

∠ C A B = ∠ F D E

(Corresponding angles are equal)
As

∠ C A B = ∠ F D E = 60^{\circ}

.
Hence, the triangles

△ A C B and △ D F E

are similar by AA similarity theorem.
The correct option is a.

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