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Theorems to Prove Congruent Triangles

Theorems to Prove Congruent Triangles. SSS - Postulate. If all the sides of one triangle are congruent to all of the sides of a second triangle, then the triangles are congruent. (SSS). p. Example #1 – SSS.

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Theorems to Prove Congruent Triangles

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  1. Theorems to Prove Congruent Triangles

  2. SSS - Postulate If all the sides of one triangle are congruent to all of the sides of a second triangle, then the triangles are congruent. (SSS)

  3. p Example #1 – SSS Use the SSS Postulate to show the two triangles are congruent. Find the length of each side. AC = 5 (2,7) BC = 7 (-2,2) (-7,2) AB = MO = 5 (9,2) NO = 7 (2,2) MN = By SSS (-7,-5)

  4. w Example 2 – SSS Let ABCD be a parallelogram and AC be one of its diagonals. Sketch a figure. What can you say about triangles ABC and CDA? Explain.

  5. Definition – Included Angle K is the angle between JK and KL. It is called the included angle of sides JK and KL. What is the included angle for sides KL and JL? L

  6. SAS - Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent. (SAS) S A S S A S by SAS

  7. p Example 3 – SAS In which pair of triangles pictured below could you use SAS to prove the triangles are congruent? Pair 4

  8. Definition – Included Side JK is the side between J and K. It is called the included side of angles J and K. What is the included side for angles K and L? KL

  9. ASA - Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent. (ASA) by ASA

  10. p Identify the Congruent Triangles. Identify the congruent triangles (if any). State the postulate by which the triangles are congruent. by SSS by SAS Note: and are not SSS, SAS, or ASA.

  11. A C B D F E AAS (Angle, Angle, Side) • If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, . . . then the 2 triangles are CONGRUENT!

  12. A C B D F E HL (Hypotenuse, Leg) ***** only used with right triangles**** • If both hypotenuses and a pair of legs of two RIGHT triangles are congruent, . . . then the 2 triangles are CONGRUENT!

  13. AAA (Angle, Angle, Angle) Is it possible to prove triangle congruence from AAA? 2 equilateral triangles

  14. Summary • Any Triangle may be proved congruent by: SSS SAS ASA AAS • Right Triangles may also be proven congruent by HL (Hypotenuse, Leg)

  15. A C B Example 4 D E F

  16. A C B D E F Example 5 • Given the markings on the diagram, is the pair of triangles congruent by one of the congruency theorems in this lesson? No ! SSA doesn’t work

  17. A C B D Example 6 • Given the markings on the diagram, is the pair of triangles congruent by one of the congruency theorems in this lesson? YES ! Use the reflexive side CB, and you have SSS

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

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

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

  21. 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:

  22. Homework Pg. 216 #12-16 even, 20 Pg. 223 #8-18 even

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