Answered: "Write the triangle similarity statement and the reason..." - Plainmath

Ernstfalld

Answered question

2021-08-11

Write the triangle similarity statement and the reason for why the triangles are similar.

△ X Y Z \sim △ ? B y : ?

Answer & Explanation

lamusesamuset

Skilled2021-08-12Added 93 answers

Step 1
Taking

△ X Y Z

∠ X = 45^{\circ}, ∠ Y = 85^{\circ}

Now,
Since sum of interior angle of triangle is

180^{\circ}

\Rightarrow ∠ X + ∠ Y + ∠ Z = 180^{\circ}

45^{\circ} + 85^{\circ} + ∠ Z = 180^{\circ}

∠ Z = 180^{\circ} - 130^{\circ}

∠ Z = 50^{\circ}

Step 2
Taking

△ W Y U

∠ W = 50^{\circ}, ∠ Y = 85^{\circ}

Now,
Since sum of interior angle of triangle is

180^{\circ}

\Rightarrow ∠ W + ∠ Y + ∠ U = 180^{\circ}

50^{\circ} + 85^{\circ} + ∠ U = 180^{\circ}

∠ U = 180^{\circ} - 135^{\circ}

∠ U = 45^{\circ}

Step 3
In

△ X Y Z and △ U Y W

∠ X = ∠ U = 50^{\circ}

∠ Y = ∠ Y = 85^{\circ}

∠ Z = ∠ W = 45^{\circ}

Therefore

△ X Y Z \sim △ U Y W

By: AA similarity

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