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4.4 - Prove Triangles Congruent by SAS and HL

4.4 - Prove Triangles Congruent by SAS and HL. Included Angle:. Angle in-between two congruent sides. 1. Use the diagram to name the included angle between the given pair of sides.  H. 1. Use the diagram to name the included angle between the given pair of sides.  HIG.

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4.4 - Prove Triangles Congruent by SAS and HL

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  1. 4.4 - Prove Triangles Congruent by SAS and HL

  2. Included Angle: Angle in-between two congruent sides

  3. 1. Use the diagram to name the included angle between the given pair of sides. H

  4. 1. Use the diagram to name the included angle between the given pair of sides. HIG

  5. 1. Use the diagram to name the included angle between the given pair of sides. JGI

  6. Side-Angle-Side (SAS) Congruence Postulate E F 4cm B C 4cm D A

  7. included If two sides and the _____________ angle of one triangle are __________ to two sides and the included angle of a second triangle, then the two triangles are ____________ congruent congruent

  8. Right Triangles: hypotenuse leg leg

  9. hypotenuse leg right congruent hypotenuse leg right congruent

  10. 2. Decide whether the triangles are congruent. Explain your reasoning. SSS Yes,

  11. 2. Decide whether the triangles are congruent. Explain your reasoning. SSS Yes,

  12. 2. Decide whether the triangles are congruent. Explain your reasoning. SAS Yes,

  13. 2. Decide whether the triangles are congruent. Explain your reasoning. AD≠ CD No,

  14. 2. Decide whether the triangles are congruent. Explain your reasoning. SAS Yes,

  15. 2. Decide whether the triangles are congruent. Explain your reasoning. HL Yes,

  16. 2. Decide whether the triangles are congruent. Explain your reasoning. Not a right triangle No,

  17. 2. Decide whether the triangles are congruent. Explain your reasoning. SSS Yes,

  18. 2. Decide whether the triangles are congruent. Explain your reasoning. SAS Yes,

  19. 3. State the third congruence that must be given to prove ABC DEF. GIVEN: BE, , ______  ______. Use the SAS Congruence Postulate.

  20. 3. State the third congruence that must be given to prove ABC DEF. GIVEN: , ______  ______. Use the SSS Congruence Postulate.

  21. 3. State the third congruence that must be given to prove ABC DEF. GIVEN: A is a right angle and AD. Use the HL Congruence Theorem.

  22. 4. Given: Prove: ∆RGI ∆TGH 1. given 1. 2. 2. Def. of midpt Def. of midpt 3. 3. RGITGH 4. 4. Vertical angles ∆RGI ∆TGH 5. SAS 5.

  23. A 5. Given: Prove: ∆ABD ∆CDB B D C 1. 1. Given

  24. A B D C

  25. A 5. Given: Prove: ∆ABD ∆CDB B D C Statements Reasons 1. 1. Given CDB  ABD 2. 2. Alternate Interior Angles 3. Given 3. 4. 4. Reflexive ∆ABD ∆CDB 5. SAS 5.

  26. A 6. Given: Prove: ∆ACD  ∆ACB D C B Statements Reasons 1. 1. Given 2. Def. of Angle Bisector 2. 3. Given 3. 4. 4. Reflexive 5. SAS ∆ACD  ∆ACB 5.

  27. A 7. Given: Prove: ∆ACD  ∆ACB D C B Statements Reasons 1. 1. Given 2. Given 2. 3. ACD and ACB are right angles 3. Def. of perp. lines 4. All right angles are  4. 5. 5. Reflexive 6. 6. HL ∆ACD  ∆ACB

  28. HW Problem # 27 Ans:

  29. HW Problem # 26

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