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Triangle Congruence: by SSS and SAS

Triangle Congruence: by SSS and SAS. Geometry (Holt 4-5) K. Santos. Side-Side-Side (SSS) Congruence Postulate (4-5-1). If the three sides of one triangle are congruent to the three sides of another triangle , then the two triangles are congruent .

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Triangle Congruence: by SSS and SAS

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  1. Triangle Congruence: by SSS and SAS Geometry (Holt 4-5) K. Santos

  2. Side-Side-Side (SSS) Congruence Postulate (4-5-1) If the three sides of one triangle are congruent to the three sides of another triangle , then the two triangles are congruent. A D Given: E B C F Then:

  3. Included Angle Included angle—is an angle formed by two adjacent sides. A B C < B is the included angle between sides and

  4. Side-Angle-Side (SAS) Congruence Postulate(4-5-2) If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. Given: A J K < A K B C L Then: Please note both angles must be included between the sides!!!

  5. Example—Writing a congruence statement Write a congruence statement for the congruent triangles and name the postulate you used to know the triangles were congruent. 1. D R S 2. A F E T B C D ADC SAS Postulate SSS Postulate

  6. Example—what other information is needed What other information do you need to prove the two triangles congruent by SSS or SAS? • M T 2. G H Q U R N O V I S Need <M <U for SAS or need for SSS need <G <Q for SAS or need for SSS

  7. Example—explain triangle congruence Use the SSS or SAS postulate to explain why the triangles are congruent. A B D C It is given: and You know: by reflexive property of congruence So: ADC CBA by SSS Postulate

  8. Example—verifying triangle congruence Show that the triangles are congruent for the given value of the variable. , a = 3 U X 4 2 a 3a - 5 W V 3 Z a – 1 Y ZY = a – 1 XZ = a XY = 3a - 5 ZY = 3 – 1 XZ =3 XY = 3(3) - 5 ZY = 2 XY = 4 So,

  9. Proof Q Given: bisects <RQS Prove: P R S Statements Reasons 1. bisects <RQS1. Given 2. < RQP < SQP 2. Definition of angle bisector 3. 3. Given 4. 4. Reflexive property of congruence 5. 5. SAS Postulate (3, 2, 4)

  10. Proof Given: E G Prove: F H Statements Reasons 1. 1. Given 2. < EGF <HFG 2. Alternate Interior Angles Theorem 3. 3. Given 4. 4. Reflexive Property of congruence 5. 5. SSS Postulate (2, 3, 4)

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