Get the solution to "If the triangles are similar write a similarity..."

postillan4

Answered question

2021-08-09

If the triangles are similar write a similarity statement.

△ ? \sim △ ?

Theodore Schwartz

Skilled2021-08-10Added 99 answers

Step 1
In

△ M I J

, we have

∠ J M I = 55^{\circ}, ∠ J I M = 90^{\circ}

We know that sum of angles in a triangle

= 180^{\circ}

.
Therefore,

∠ J M I + ∠ J I M + ∠ M J I = 180^{\circ}

55^{\circ} + 90^{\circ} + ∠ M J I = 180^{\circ}

145^{\circ} + ∠ M J I = 180^{\circ}

∠ M J I = 180^{\circ} - 145^{\circ}

∠ M J I = 35^{\circ}

△ J I K

, we have

∠ J I K = 90^{\circ}, ∠ J K I = 35^{\circ}

Step 2
In

△ M J I and △ J I K

∠ J I M = ∠ J I K = 90^{\circ}

∠ M J I = ∠ J K I = 35^{\circ}

We know that if two angles of one triangle are congruent to two angles in another triangle then the two triangles are similar.
Hence,

△ J M I \sim △ K J I

(By AA- similarity criteria)

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