Question

for each figure below, determine (by using the markings) if there is a pair of congruent triangles. if there is, name the congruence and give the property justifying the congruence.
note that the pairs of triangles are drawn as congruent, but you should not rely on how they are drawn in determining your answers. if necessary, you may learn what the markings on a figure indicate.
(a)
(b)
congruent:
not necessarily congruent
\\( \triangle u v w \cong \triangle \square \\) by the
select

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. In the figure, the angles at point \(A\) (where the two triangles intersect) are vertical angles. Let's call them \(\angle UAW\) and \(\angle XAY\). So, \(\angle UAW=\angle XAY\).

Step2: Check given congruent parts

We are given that one pair of sides is congruent (marked with the same tick - mark) and one pair of angles is congruent (\(\angle W=\angle X\)).

Step3: Apply the ASA (Angle - Side - Angle) congruence criterion

The ASA congruence criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
In \(\triangle UVW\) and \(\triangle XYZ\) (assuming the correct triangle names based on the vertices), we have \(\angle W=\angle X\), the included side (the side between the two angles) is congruent (from the tick - marks), and \(\angle UAW = \angle XAY\) (vertical angles).

Answer:

\(\triangle UVW\cong\triangle XYZ\) by the \(ASA\) (Angle - Side - Angle) congruence criterion.