Question

consider the diagram.
part a
select the correct answer choice from each drop - down list to make the statement true.
△xyz is to △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 measure of \(\angle XZY\) and \(\angle TZW\)

Since \(\angle XZW = 133^{\circ}\), and \(\angle XZY+\angle XZW = 180^{\circ}\) (linear - pair of angles), then \(\angle XZY=180^{\circ}- 133^{\circ}=47^{\circ}\). Also, \(\angle TZW = 47^{\circ}\) (vertically - opposite angles to \(\angle XZY\)).

Step2: Find the measure of \(\angle XYZ\)

In \(\triangle XYZ\), we know \(\angle YXZ = 43^{\circ}\), \(\angle XZY = 47^{\circ}\). Using the angle - sum property of a triangle (\(\angle YXZ+\angle XZY+\angle XYZ = 180^{\circ}\)), we get \(\angle XYZ=180^{\circ}-(43^{\circ}+47^{\circ}) = 90^{\circ}\).
In \(\triangle T W Z\), \(\angle WTZ = 43^{\circ}\), \(\angle TZW = 47^{\circ}\). Using the angle - sum property of a triangle (\(\angle WTZ+\angle TZW+\angle T W Z=180^{\circ}\)), we get \(\angle T W Z=180^{\circ}-(43^{\circ}+47^{\circ}) = 90^{\circ}\).

Step3: Check for similarity

We have \(\angle YXZ=\angle WTZ = 43^{\circ}\), \(\angle XZY=\angle TZW = 47^{\circ}\), \(\angle XYZ=\angle T W Z = 90^{\circ}\). By the AA (angle - angle) similarity criterion, if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

Answer:

\(\triangle XYZ\) is similar to \(\triangle T W Z\) because the two triangles have two pairs of congruent angles.