Question

multiple choice 1 point
choose the statement that indicates that the pair of triangles are congruent:

Explanation:

Step1: Match corresponding vertices

In congruent triangles, corresponding vertices (and thus angles and sides) must match.
In \(\triangle XWV\), vertex \(X\) has an angle marked with a double - arc. In \(\triangle CED\), vertex \(E\) has a double - arc angle. But wait, no. Let's check side - angle - side.
Looking at \(\triangle XWV\):

• The side between the single - arc and double - arc angles:

In \(\triangle XWV\), if we consider the order of angles (single - arc at \(W\), double - arc at \(X\), and the other single - arc at \(V\)).
In \(\triangle CED\), single - arc at \(C\), double - arc at \(E\), and single - arc at \(D\) is not correct.
Wait, using the side - side - side (if we assume the tick - marks represent equal sides) or angle - side - angle.
Let's check the vertex order:
In \(\triangle XWV\), if we map the angles (by their markings) to \(\triangle CED\) (incorrect).
Wait, actually, using the congruence notation \(\triangle ABC\cong\triangle DEF\) means \(A\) corresponds to \(D\), \(B\) corresponds to \(E\), \(C\) corresponds to \(F\).
Looking at \(\triangle XWV\) and \(\triangle CED\):
If we consider the side lengths (by tick - marks) and angle markings:
The side with one tick in \(\triangle XWV\) (say \(XW\)) and the side with one tick in \(\triangle CED\) (say \(CE\)) is wrong. Wait, no.
Wait, using the angle - side - angle (if we assume the angles with same markings are equal).
In \(\triangle XWV\), the angles: let's assume the single - arc at \(W\), double - arc at \(X\), and single - arc at \(V\).
In \(\triangle CED\), if we consider \(\triangle XWV\cong\triangle CED\):
\(X\) (double - arc) corresponds to \(E\) (double - arc), \(W\) (single - arc) corresponds to \(C\) (single - arc), \(V\) (single - arc) corresponds to \(D\) (single - arc) is wrong.
Wait, no, using the congruence of triangles:
If we use the fact that in congruent triangles, the order of the letters matters.
In \(\triangle XWV\) and \(\triangle CED\):
If we check the side - angle - side (assuming the tick - marks for sides and angle - marks for angles):
\(\triangle XWV\) has sides (by tick - marks) and angles.
Wait, another approach:
The congruent triangles \(\triangle XWV\) and \(\triangle CED\):
\(XW = CE\) (by tick - marks, assume two ticks), \(WV=ED\) (by tick - marks, assume one tick), \(XV = CD\) (by tick - marks, assume three ticks). And angles: \(\angle W=\angle C\) (single - arc), \(\angle X=\angle E\) (double - arc), \(\angle V=\angle D\) (single - arc).

Answer:

\(\triangle XWV\cong\triangle CED\)