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.
your answer
(a)
not necessarily congruent
congruent:
△mno≅△□ by the
select
(b)
not necessarily congruent
congruent:
△ghi≅△□ by the
select
(c)
not necessarily congruent
congruent:
△uvw≅△□ by the
select

Explanation:

Step1: Recall triangle congruence properties

The main triangle congruence properties are SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), and HL (Hypotenuse - Leg for right - angled triangles).

Step2: Analyze part (a)

In \(\triangle MNO\) and \(\triangle PRQ\), we cannot match the sides and angles based on the given markings to satisfy any of the congruence properties.

Step3: Analyze part (b)

In \(\triangle GHI\) and \(\triangle JKL\), we have two sides and the included angle. Let's assume the marked side - angle - side. If \(GH = JK\), \(\angle G=\angle K\), and \(GI = KL\) (from the markings), then by the SAS (Side - Angle - Side) property \(\triangle GHI\cong\triangle JKL\).

Step4: Analyze part (c)

In \(\triangle UVW\) and \(\triangle ZYX\), we have two angles and a non - included side. If \(\angle U=\angle X\), \(\angle W=\angle Y\), and \(UV = ZY\) (from the markings), then by the AAS (Angle - Angle - Side) property \(\triangle UVW\cong\triangle ZYX\).

Answer:

(a) Not Necessarily Congruent
(b) Congruent: \(\triangle GHI\cong\triangle JKL\) by the SAS (Side - Angle - Side)
(c) Congruent: \(\triangle UVW\cong\triangle ZYX\) by the AAS (Angle - Angle - Side)