Question

given the isosceles triangle, identify a pair of congruent sides. the options are: \\(\overline{ca}\\) and \\(\overline{aw}\\); \\(\overline{cw}\\) and \\(\overline{aw}\\); \\(\overline{ca}\\) and \\(\overline{cw}\\); there are no congruent sides.

Explanation:

Step1: Recall Isosceles Triangle Definition

An isosceles triangle has at least two congruent (equal - length) sides. In a right - isosceles triangle (since there is a right angle at \(W\)), the legs (the sides forming the right angle) are congruent.

Step2: Identify Sides in the Triangle

In triangle \(ACW\), \(\angle W = 90^{\circ}\), \(\angle A\) and \(\angle C\) are the other two angles. The sides forming the right angle are \(\overline{CW}\) and \(\overline{AW}\). Since it is an isosceles triangle, these two legs should be congruent. Also, from the check - mark in the option, \(\overline{CW}\) and \(\overline{AW}\) is the correct pair of congruent sides.

Answer:

B. \(\overline{CW}\) and \(\overline{AW}\) (assuming the option with \(\overline{CW}\) and \(\overline{AW}\) is option B, if we follow the marking in the image where \(\overline{CW}\) and \(\overline{AW}\) is checked)