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 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)
not necessarily congruent
congruent:
△abc≅△ by the

(b)
not necessarily congruent
congruent:
△uvw≅△ by the

(c)
not necessarily congruent
congruent:
△ghi≅△ by the

Explanation:

Step1: Identify congruence criteria

Congruent triangles can be proven by SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side) and HL (Hypotenuse - Leg for right - triangles).

Step2: Analyze figure (a)

In \(\triangle ABC\) and \(\triangle FED\), we have \(AB = FE\), \(\angle B=\angle E\), \(BC = ED\). By the SAS (Side - Angle - Side) congruence criterion, \(\triangle ABC\cong\triangle FED\).

Step3: Analyze figure (b)

In \(\triangle UVW\) and \(\triangle XZY\), we have \(UV = XZ\), \(VW=ZY\), \(UW = XY\). By the SSS (Side - Side - Side) congruence criterion, \(\triangle UVW\cong\triangle XZY\).

Step4: Analyze figure (c)

In \(\triangle GHI\) and \(\triangle JKE\), we have \(\angle G=\angle J\), \(GI = JE\), \(\angle I=\angle E\). By the ASA (Angle - Side - Angle) congruence criterion, \(\triangle GHI\cong\triangle JKE\).

Answer:

(a) Congruent: \(\triangle ABC\cong\triangle FED\) by the SAS
(b) Congruent: \(\triangle UVW\cong\triangle XZY\) by the SSS
(c) Congruent: \(\triangle GHI\cong\triangle JKE\) by the ASA