Question

9 - 26 quiz (triangle congruence) complete each congruence statement by naming the corresponding angle or side. 1) △gfe≅△gfv 2) △wml≅△wmx 3) △xwv≅△ijw 4) △fge≅△fij gf¯≅? ∠w≅? ∠nml≅? fg¯≅?

Explanation:

1. For \(\triangle GFE\cong\triangle GFV\):

• # Explanation:
• ## Step1: Identify corresponding sides
• In congruent - triangles, corresponding sides are equal. Since \(\triangle GFE\cong\triangle GFV\), the side corresponding to \(\overline{GF}\) is \(\overline{GF}\) itself (common side). And the side corresponding to \(\overline{FE}\) is \(\overline{FV}\), and the side corresponding to \(\overline{GE}\) is \(\overline{GV}\). So, \(\overline{GF}\cong\overline{GF}\), \(\overline{FE}\cong\overline{FV}\), \(\overline{GE}\cong\overline{GV}\).
• # Answer: \(\overline{GF}\cong\overline{GF}\), \(\overline{FE}\cong\overline{FV}\), \(\overline{GE}\cong\overline{GV}\)

1. For \(\triangle WML\cong\triangle WMX\):

• # Explanation:
• ## Step1: Identify corresponding angles
• In congruent triangles \(\triangle WML\cong\triangle WMX\), the angle corresponding to \(\angle WML\) is \(\angle WMX\), the angle corresponding to \(\angle MLW\) is \(\angle M XW\), and the angle corresponding to \(\angle LWM\) is \(\angle XWM\). Also, the side - corresponding relationships hold: \(\overline{WM}\cong\overline{WM}\) (common side), \(\overline{ML}\cong\overline{MX}\), \(\overline{LW}\cong\overline{XW}\).
• # Answer: \(\angle WML\cong\angle WMX\), \(\angle MLW\cong\angle M XW\), \(\angle LWM\cong\angle XWM\), \(\overline{WM}\cong\overline{WM}\), \(\overline{ML}\cong\overline{MX}\), \(\overline{LW}\cong\overline{XW}\)

1. For \(\triangle XWV\cong\triangle IJV\):

• # Explanation:
• ## Step1: Identify corresponding angles
• Since \(\triangle XWV\cong\triangle IJV\), the angle corresponding to \(\angle W\) is \(\angle J\) (by the order of the congruence statement). Also, \(\angle X\) corresponds to \(\angle I\) and \(\angle V\) is common to both triangles. For sides, \(\overline{XW}\cong\overline{IJ}\), \(\overline{WV}\cong\overline{JV}\), \(\overline{XV}\cong\overline{IV}\).
• # Answer: \(\angle W\cong\angle J\), \(\angle X\cong\angle I\), \(\angle V\cong\angle V\), \(\overline{XW}\cong\overline{IJ}\), \(\overline{WV}\cong\overline{JV}\), \(\overline{XV}\cong\overline{IV}\)

1. For \(\triangle FGE\cong\triangle FIJ\):

• # Explanation:
• ## Step1: Identify corresponding sides
• In \(\triangle FGE\cong\triangle FIJ\), the side corresponding to \(\overline{FG}\) is \(\overline{FI}\), the side corresponding to \(\overline{GE}\) is \(\overline{IJ}\), and the side corresponding to \(\overline{FE}\) is \(\overline{FJ}\). Also, for angles, \(\angle F\) is common, \(\angle G\) corresponds to \(\angle I\), and \(\angle E\) corresponds to \(\angle J\).
• # Answer: \(\overline{FG}\cong\overline{FI}\), \(\overline{GE}\cong\overline{IJ}\), \(\overline{FE}\cong\overline{FJ}\), \(\angle F\cong\angle F\), \(\angle G\cong\angle I\), \(\angle E\cong\angle J\)

Answer:

1. For \(\triangle GFE\cong\triangle GFV\):

• # Explanation:
• ## Step1: Identify corresponding sides
• In congruent - triangles, corresponding sides are equal. Since \(\triangle GFE\cong\triangle GFV\), the side corresponding to \(\overline{GF}\) is \(\overline{GF}\) itself (common side). And the side corresponding to \(\overline{FE}\) is \(\overline{FV}\), and the side corresponding to \(\overline{GE}\) is \(\overline{GV}\). So, \(\overline{GF}\cong\overline{GF}\), \(\overline{FE}\cong\overline{FV}\), \(\overline{GE}\cong\overline{GV}\).
• # Answer: \(\overline{GF}\cong\overline{GF}\), \(\overline{FE}\cong\overline{FV}\), \(\overline{GE}\cong\overline{GV}\)

1. For \(\triangle WML\cong\triangle WMX\):

• # Explanation:
• ## Step1: Identify corresponding angles
• In congruent triangles \(\triangle WML\cong\triangle WMX\), the angle corresponding to \(\angle WML\) is \(\angle WMX\), the angle corresponding to \(\angle MLW\) is \(\angle M XW\), and the angle corresponding to \(\angle LWM\) is \(\angle XWM\). Also, the side - corresponding relationships hold: \(\overline{WM}\cong\overline{WM}\) (common side), \(\overline{ML}\cong\overline{MX}\), \(\overline{LW}\cong\overline{XW}\).
• # Answer: \(\angle WML\cong\angle WMX\), \(\angle MLW\cong\angle M XW\), \(\angle LWM\cong\angle XWM\), \(\overline{WM}\cong\overline{WM}\), \(\overline{ML}\cong\overline{MX}\), \(\overline{LW}\cong\overline{XW}\)

1. For \(\triangle XWV\cong\triangle IJV\):

• # Explanation:
• ## Step1: Identify corresponding angles
• Since \(\triangle XWV\cong\triangle IJV\), the angle corresponding to \(\angle W\) is \(\angle J\) (by the order of the congruence statement). Also, \(\angle X\) corresponds to \(\angle I\) and \(\angle V\) is common to both triangles. For sides, \(\overline{XW}\cong\overline{IJ}\), \(\overline{WV}\cong\overline{JV}\), \(\overline{XV}\cong\overline{IV}\).
• # Answer: \(\angle W\cong\angle J\), \(\angle X\cong\angle I\), \(\angle V\cong\angle V\), \(\overline{XW}\cong\overline{IJ}\), \(\overline{WV}\cong\overline{JV}\), \(\overline{XV}\cong\overline{IV}\)

1. For \(\triangle FGE\cong\triangle FIJ\):

• # Explanation:
• ## Step1: Identify corresponding sides
• In \(\triangle FGE\cong\triangle FIJ\), the side corresponding to \(\overline{FG}\) is \(\overline{FI}\), the side corresponding to \(\overline{GE}\) is \(\overline{IJ}\), and the side corresponding to \(\overline{FE}\) is \(\overline{FJ}\). Also, for angles, \(\angle F\) is common, \(\angle G\) corresponds to \(\angle I\), and \(\angle E\) corresponds to \(\angle J\).
• # Answer: \(\overline{FG}\cong\overline{FI}\), \(\overline{GE}\cong\overline{IJ}\), \(\overline{FE}\cong\overline{FJ}\), \(\angle F\cong\angle F\), \(\angle G\cong\angle I\), \(\angle E\cong\angle J\)