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5.5/5.6 Proving Triangles Congruent

5.5/5.6 Proving Triangles Congruent. SSS and SAS. What You'll Learn. You will learn to use the SSS and SAS tests for congruency. B. A. C. 2) Construct a segment congruent to AC. Label the endpoints of the segment D and E. 3) Construct a segment congruent to AB.

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5.5/5.6 Proving Triangles Congruent

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  1. 5.5/5.6 Proving Triangles Congruent

  2. SSS and SAS What You'll Learn You will learn to use the SSS and SAS tests for congruency.

  3. B A C 2) Construct a segment congruent to AC. Label the endpoints of the segment D and E. 3) Construct a segment congruent to AB. 4) Construct a segment congruent to CB. F 6) Draw DF and EF. D E SSS and SAS 5) Label the intersection F. 1) Draw an acute scalene triangle on a piece of paper. Label its vertices A, B, and C, on the interior of each angle. This activity suggests the following postulate.

  4. S B ST RS and RT and If AC  T C R A BC  AB  SSS and SAS three sides corresponding then ΔABC ΔRST

  5. In two triangles, ZY  FE, XY  DE, and XZ  DF. X D Y E Z F SSS and SAS Write a congruence statement for the two triangles. Sample Answer: ΔZXY ΔFDE

  6. C is the included angle of CA and CB C A B B is the included angle of BA and BC A is the included angle of AB and AC SSS and SAS In a triangle, the angle formed by two given sides is called the ____________ of the sides. included angle Using the SSS Postulate, you can show that two triangles are congruent if theircorresponding sides are congruent. You can also show their congruence by using two sides and the ____________. included angle

  7. S B RS RT and If AC  T C R A AB  SSS and SAS included angle two sides A  R and then ΔABC ΔRST

  8. Q D R F E P D is not the included angle for DF and EF. SSS and SAS On a piece of paper, write your response to the following: Determine whether the triangles are congruent by SAS. • If so, write a statement of congruence and tell why they are congruent. • If not, explain your reasoning. NO!

  9. End of Section 5.5

  10. ASA and AAS What You'll Learn You will learn to use the ASA and AAS tests for congruency.

  11. C AC is the included side of A and C CB is the included side of C and B AB is the included side of A and B A B ASA and AAS The side of a triangle that falls between two given angles is called the___________ of the angles. included side It is the one side common to both angles. You can show that two triangles are congruent by using _________ and the ___________ of the triangles. two angles included side

  12. S B RT and T C R A AC  ASA and AAS included side two angles C  T If A  R and then ΔABC ΔRST

  13. CA and CB are the nonincluded sides of A and B C A B ASA and AAS You can show that two triangles are congruent by using _________ and a ______________. two angles nonincluded side

  14. S B TS T C R A CB  ASA and AAS nonincluded side two angles C  T and If A  R and then ΔABC ΔRST

  15. L D If F and M are marked congruent, then FE and MN would be included sides. M F N E ASA and AAS ΔDEF and ΔLNM have one pair of sides and one pair of angles marked to show congruence. What other pair of angles must be marked so that the two triangles are congruent by AAS? However, AAS requires the nonincluded sides. Therefore, D and L must be marked.

  16. End of Section 5.6

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