Question

similarity - item 35517
complete the statement below about the two figures.
two triangles: triangle abc with angles at a: 67°, b: 81°, c: 32°; triangle xyz with angles at y: 66°, x: 59°, z: 55°
they are ▼ because their corresponding angles are ▼.

Explanation:

Step1: Calculate sum of angles in each triangle

For \(\triangle ABC\): \(67^\circ + 81^\circ + 32^\circ = 180^\circ\) (valid triangle).
For \(\triangle XYZ\): \(66^\circ + 59^\circ + 55^\circ = 180^\circ\) (valid triangle).

Step2: Compare corresponding angles

• \(\angle A = 67^\circ\) vs \(\angle X = 59^\circ\) (not equal).
• \(\angle B = 81^\circ\) vs \(\angle Y = 66^\circ\) (not equal).
• \(\angle C = 32^\circ\) vs \(\angle Z = 55^\circ\) (not equal).

Since corresponding angles are not equal, the triangles are not similar.

Answer:

They are \(\boldsymbol{\text{not similar}}\) because their corresponding angles are \(\boldsymbol{\text{not equal}}\).