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Triangle Congruence

Triangle Congruence. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…. IN ORDER FOR TWO TRIANGLES TO BE CONGRUENT ALL CORRESPONDING ANGLES AND SIDES MUST BE CONGRUENT!. Congruency Statement ΔABC≅ Δ DEF

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Triangle Congruence

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  1. TriangleCongruence

  2. Define congruent…. Triangle ABC is congruent to Triangle FED. Name 6 congruent parts…

  3. IN ORDER FOR TWO TRIANGLES TO BE CONGRUENT ALL CORRESPONDING ANGLES AND SIDES MUST BE CONGRUENT! Congruency Statement ΔABC≅ΔDEF Based on the congruency statement, which angles and which sides must be congruent?

  4. Complete the congruency statement for the following triangles… ΔPQR≅Δ_______________ ΔPQR≅Δ_______________

  5. Corresponding Parts • AB  • BC  • AC  •  A  •  B  •  C  B A C E F D Name the corresponding congruent parts for these triangles. ABC DEF

  6. SSS SAS ASA AAS Do you need all six ? NO !

  7. Side-Side-Side (SSS) E B F A D C • AB DE • BC EF • AC DF ABC DEF If three sides of one triangle are congruent to three corresponding sides of a second triangle, then the triangles are congruent.

  8. COMERCIAL BREAK!!! http://www.youtube.com/watch?v=o009kN8bCC8

  9. Included Angle The angle between two sides H G I

  10. E Y S Included Angle The included angle is the angle with the letter that both sides share Name the included angle: YE and ES ES and YS YS and YE E S Y

  11. Side-Angle-Side (SAS) If two sides of one triangle and the included angle are congruent the two corresponding sides and included angle, then the triangles are congruent. B E F A C D • AB DE • A D • AC DF ABC DEF included angle

  12. COMERCIAL BREAK!!! http://www.youtube.com/watch?v=4GZtALwvRaE&feature=grec_index

  13. Included Side The side between two angles GI GH HI

  14. E Y S Included Side Name the included angle: Y and E E and S S and Y YE ES SY

  15. Angle-Side-Angle (ASA) If two angles of a triangle and the included side are congruent the corresponding angles and included side, then the triangles are congruent. B E F A C D • A D • AB  DE • B E ABC DEF included side

  16. Angle-Angle-Side (AAS) If two angles of a triangle and the non-included side are congruent the corresponding angles and non-included side, then the triangles are congruent. B E F A C D • A D • B E • BC  EF ABC DEF Non-included side

  17. Side Names of Triangles leg hypotenuse leg • Right Triangles: side across from right angle is the hypotenuse, the remaining two are legs.

  18. Examples: Tell whether the segment is a leg or a hypotenuse.

  19. Hypotenuse- Leg (HL) Congruence Theorem: • If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then the two triangles are congruent. • Example: because of HL. A X B C Y Z

  20. Examples: Determine if the triangles are congruent. State the postulate or theorem.

  21. There are 5 ways to prove triangles are congruent… • Each of these ways have 3 things to look for! • ASA • SAS • SSS • AAS • HL (Right Triangle)

  22. Warning: No ASS or SSA Postulate NO CURSING IN MATH CLASS! There is no such thing as an SSA postulate! E B F A C D NOT CONGRUENT

  23. Warning: No AAA Postulate There is no such thing as an AAA postulate! E B A C F D NOT CONGRUENT

  24. SSS correspondence • ASA correspondence • SAS correspondence • AAS correspondence • HL correspondence • SSA correspondence • AAA correspondence The Congruence Postulates

  25. COMERCIAL BREAK!!! http://www.youtube.com/watch?v=hQYfCWak-Q0

  26. Name That Postulate (when possible) SAS ASA SSA SSS

  27. Name That Postulate (when possible) AAA ASA SSA SAS

  28. Name That Postulate (when possible) Vertical Angles Reflexive Property SAS SAS Reflexive Property Vertical Angles SSA SAS

  29. You try! Name That Postulate (when possible)

  30. You try! Name That Postulate (when possible)

  31. Let’s Practice ACFE Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: B D For SAS: AF For AAS:

  32. You Try! Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:

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