Question

similarity - item 35517
complete the statement below about the two figures.
they are because their corresponding angles are not congruent congruent

Explanation:

Step1: Calculate the third angle of triangle \(ABC\)

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle ABC\), let the third angle be \(A\). Using the formula \(A + B + C=180^{\circ}\), we substitute \(B = 81^{\circ}\) and \(C = 32^{\circ}\). So \(A=180^{\circ}-(81^{\circ}+32^{\circ}) = 67^{\circ}\).

Step2: Calculate the third angle of triangle \(XYZ\)

For \(\triangle XYZ\), using the angle - sum formula \(X + Y+Z = 180^{\circ}\). Substitute \(Y = 66^{\circ}\) and \(Z = 55^{\circ}\). Then \(X=180^{\circ}-(66^{\circ}+55^{\circ})=59^{\circ}\).

Step3: Compare the angles

The angles of \(\triangle ABC\) are \(67^{\circ},81^{\circ},32^{\circ}\) and the angles of \(\triangle XYZ\) are \(59^{\circ},66^{\circ},55^{\circ}\). Since no pair of corresponding angles are equal (e.g., \(67^{\circ}
eq59^{\circ}\), \(81^{\circ}
eq66^{\circ}\), \(32^{\circ}
eq55^{\circ}\)).

Answer:

They are not congruent because their corresponding angles are not congruent.