Question

are the triangles below similar?
triangle tsr: side ts=12, sr=20, rt=24; angles at t: 56°, at s: 94°, at r: 30°.
triangle xyz: side xy=15, yz=30, zx=25; angles at x: 94°, at y: 56°, at z: 30°.
options: yes, no

Explanation:

Step1: Check Angle Similarity

In triangle \( TRS \), angles are \( 56^\circ \), \( 94^\circ \), \( 30^\circ \). In triangle \( XYZ \), angles are \( 56^\circ \), \( 94^\circ \), \( 30^\circ \) (since \( 180 - 56 - 94 = 30 \)). So all angles are equal (AA similarity criterion).

Step2: Check Side Ratios

Ratios: \( \frac{12}{15} = \frac{4}{5} \), \( \frac{20}{25} = \frac{4}{5} \), \( \frac{24}{30} = \frac{4}{5} \). All side ratios are equal (SSS similarity, as angles are equal and sides proportional).

Answer:

yes