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Mathematics - Congruence

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Ayhie Flamers

This document discusses congruence in geometry. It defines congruent figures as those where corresponding sides are equal in length and corresponding angles are equal in measure. The conditions for congruence are: (1) all sides of one figure are equal to the corresponding sides of the other, (2) the angles of one figure are equal to the corresponding angles of the other, and (3) the shapes of both figures are the same. Methods for proving triangles are congruent include side-side-side, side-angle-side, and angle-side-angle. An example problem demonstrates using corresponding angles and sides to prove two triangles are congruent.

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Congruence  Congruent •The Conditions • Congruent Triangles • How to prove that • Exercise’s example Click what you want to learn
Conditions of Congruent a) The all sides of corresponding sides are equal The Conditions for b) The angles of Congruent of Corresponding sides Two Plane Figures are: are equal c) The shapes of both figure are same
Conditions of Congruent The example: A D a) The Corresponding sides a) (look the same sign) are: C B F E AC with DF, AB with R U V DE, and BC with EF b) b) Equal angle of S T Corresponding side: W <R with <W, <S with c) <V, and <T with <U c) Both of Plane Figures are Triangle
Prove Congruent Figures To Prove that 2 Triangles are Congruent: A 6cm a) Side, Side, Side T U The all sides are in equal 7cm 7cm 5cm 5cm B S C 6cm
Prove Congruent Figures To Prove that 2 Triangles are Congruent: A 6cm U b) Two Sides, One Angle T 45 The angle coincided by two 7cm 7cm sides (AB and BC or UT and TS) 45 B 6cm S C
Prove Congruent Figures A 6cm To Prove that 2 Triangles are T 45 90 U Congruent: c) Two Angles, One Side 45 1. The angles known on the 90 B S C 6cm side A 6cm 2.The side face to one of two T 90 U 55 angles 55 90 6cm B S C
Example Answer: We prove it based on the condition, that we have learn before. We look for the same C B sign: E • <CAE equal to <EBD • CE equal to ED A • <CEA equal to <BED (It hasn’t D sign, but it’s vertical angles Prove that ACE and BDE The Conclusion: ACE are congruent and BDE are congruent

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Mathematics - Congruence

  • 1. Congruence  Congruent •The Conditions • Congruent Triangles • How to prove that • Exercise’s example Click what you want to learn
  • 2. Conditions of Congruent a) The all sides of corresponding sides are equal The Conditions for b) The angles of Congruent of Corresponding sides Two Plane Figures are: are equal c) The shapes of both figure are same
  • 3. Conditions of Congruent The example: A D a) The Corresponding sides a) (look the same sign) are: C B F E AC with DF, AB with R U V DE, and BC with EF b) b) Equal angle of S T Corresponding side: W <R with <W, <S with c) <V, and <T with <U c) Both of Plane Figures are Triangle
  • 4. Prove Congruent Figures To Prove that 2 Triangles are Congruent: A 6cm a) Side, Side, Side T U The all sides are in equal 7cm 7cm 5cm 5cm B S C 6cm
  • 5. Prove Congruent Figures To Prove that 2 Triangles are Congruent: A 6cm U b) Two Sides, One Angle T 45 The angle coincided by two 7cm 7cm sides (AB and BC or UT and TS) 45 B 6cm S C
  • 6. Prove Congruent Figures A 6cm To Prove that 2 Triangles are T 45 90 U Congruent: c) Two Angles, One Side 45 1. The angles known on the 90 B S C 6cm side A 6cm 2.The side face to one of two T 90 U 55 angles 55 90 6cm B S C
  • 7. Example Answer: We prove it based on the condition, that we have learn before. We look for the same C B sign: E • <CAE equal to <EBD • CE equal to ED A • <CEA equal to <BED (It hasn’t D sign, but it’s vertical angles Prove that ACE and BDE The Conclusion: ACE are congruent and BDE are congruent