Question

are these triangles similar?
triangle ijk with angle at j: 36°, angle at k: 50°.
triangle vwu with angle at v: 50°, angle at w: 36°.
options: yes, no

Explanation:

Step1: Recall triangle similarity rule

For triangles to be similar, their corresponding angles must be equal (AA - Angle - Angle criterion). The sum of angles in a triangle is \(180^\circ\).

Step2: Calculate the third angle for \(\triangle IJK\)

In \(\triangle IJK\), we know two angles: \(\angle J = 36^\circ\) and \(\angle K = 50^\circ\). The third angle \(\angle I=180^\circ - 36^\circ - 50^\circ = 94^\circ\).

Step3: Calculate the third angle for \(\triangle VWU\)

In \(\triangle VWU\), we know two angles: \(\angle W = 36^\circ\) and \(\angle V = 50^\circ\). The third angle \(\angle U = 180^\circ - 36^\circ - 50^\circ=94^\circ\).

Step4: Check corresponding angles

Now, let's match the angles:

• \(\angle J = 36^\circ=\angle W\)
• \(\angle K = 50^\circ=\angle V\)
• \(\angle I = 94^\circ=\angle U\)

Since all three corresponding angles are equal, by AA (or AAA) criterion, the triangles are similar.

Answer:

yes