Question

are the triangles below similar?
triangle igh: side ig=20, side gh=12, side ih=24; angle at i is 30°, angle at g is 94°, angle at h is 56°.
triangle tvu: side tv=25, side vu=29, side ut=15; angle at t is 89°, angle at v is 31°, angle at u is marked with a cursor (presumably a typo, maybe 60°? but as per ocr, its 6⇧ which might be a display error).
options: yes, no

Explanation:

Step1: Check angles of first triangle

Sum of angles in a triangle is \(180^\circ\). For \(\triangle IGH\): \(30^\circ + 94^\circ + 56^\circ = 180^\circ\), angles are \(30^\circ\), \(94^\circ\), \(56^\circ\).

Step2: Check angles of second triangle

For \(\triangle TUV\): \(89^\circ + 31^\circ + \angle U = 180^\circ\), so \(\angle U = 180 - 89 - 31 = 60^\circ\)? Wait, no, wait the first triangle's angles: \(30\), \(56\), \(94\). Second triangle: \(89\), \(31\), and let's recalculate \(\angle U\): \(180 - 89 - 31 = 60^\circ\)? Wait, no, maybe I miscalculated. Wait first triangle: \(30 + 56 + 94 = 180\) (30+56=86, 86+94=180). Second triangle: angles are \(89^\circ\), \(31^\circ\), and the third angle: \(180 - 89 - 31 = 60^\circ\). Now, the angles of first triangle: \(30^\circ\), \(56^\circ\), \(94^\circ\). Second: \(31^\circ\), \(89^\circ\), \(60^\circ\). No two angles are equal between the triangles, so by AA (Angle - Angle) similarity criterion, since no two angles match, the triangles are not similar. Also, check side ratios: For \(\triangle IGH\), sides are 12, 20, 24. Ratios: \(12/15 = 0.8\), \(20/25 = 0.8\), \(24/29 \approx 0.827\). Not all ratios equal. So angles don't match, sides ratios not all equal. So not similar.

Answer:

no