Question

part a
select the correct answer choice from each drop - down list to make the statement true.
\triangle xyz is
\triangle twz because the two triangles have
part b
select the correct answer choice from each drop - down list to make the statement true.

Explanation:

Step1: Find the third angle of \(\triangle XYZ\)

In \(\triangle XYZ\), we know one angle is \(43^{\circ}\) and the angle at \(Z\) (supplementary to \(133^{\circ}\)) is \(180 - 133=47^{\circ}\). Using the angle - sum property of a triangle (\(A + B + C=180^{\circ}\)), the third angle \(\angle XYZ=180-(43 + 47)=90^{\circ}\)

Step2: Find the third angle of \(\triangle TWZ\)

In \(\triangle TWZ\), we know one angle is \(43^{\circ}\) and another is \(18^{\circ}\). Using the angle - sum property of a triangle (\(A + B + C = 180^{\circ}\)), the third angle \(\angle TWZ=180-(43 + 18)=119^{\circ}\). Wait, no, we should use the vertical - angle and angle - sum property. The vertical angle at \(Z\) is \(133^{\circ}\). For \(\triangle TWZ\), if we consider the angles: one angle is \(43^{\circ}\), and using the fact that \(\angle XZW = 133^{\circ}\), then the non - adjacent angles. Actually, we use the AA (angle - angle) similarity criterion. \(\angle XZY=\angle WZT\) (vertical angles). \(\angle YXZ=\angle WTZ = 43^{\circ}\)

Answer:

\(\triangle XYZ\) is similar to \(\triangle TWZ\) because the two triangles have two pairs of congruent angles (AA similarity criterion)