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GEOMETRY: Chapter 4

GEOMETRY: Chapter 4. 4.3: Prove Triangles Congruent by SSS and SAS. Postulate 19: Side-Side-Side (SSS) Congruence Postulate If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

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GEOMETRY: Chapter 4

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  1. GEOMETRY: Chapter 4 4.3: Prove Triangles Congruent by SSS and SAS

  2. Postulate 19: Side-Side-Side (SSS) Congruence Postulate If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 234.

  3. Ex. 1: Use the SSS Congruence Postulate Prove: Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 235.

  4. Ex. 2. Which are the coordinates of the vertices of a triangle congruent to triangle XYZ? • (6, 2), (0, -6), (6, -5) • (5, 1), (-1, -6), (5, -6) • (4, 0), (-1, -7), (4, -7) • (3, -1), (-3, -7), (3, -8) Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 235.

  5. Ex. 2 (cont.) First, we need to find the distance of each side of the given triangle. The distance from (-3, 2) to (-3, -4) is 6. The distance from (-3, -4) to (4, -4) is 7. The distance from (-3, 2) to (4, -4) is:

  6. Ex. 2 (cont.) Then I need to look at the choices and see which two points give me two sides with lengths 6 and 7 units. The only one that fits this requirement is B. The distance from (-1, -6) to (5, -6) is 6. The distance from (5, 1) to (5, -6) is 7. Last step: check to find out if the hypotenuse of B is equal to the hypotenuse in the given triangle XYZ. Using the SSS Congruence Postulate, Choice B gives me the vertices (coordinates) of the congruent triangle.

  7. Ex. 3: The opposite sides of the gate are the same length. How would you put a brace on the gate to be sure that the gate keeps its shape. Diagonally, since the triangles will be rigid and, by the SSS Congruence Postulate, cannot change shape. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 236.

  8. Postulate 20: Side-Angle-Side (SAS) Congruence 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 two triangles are congruent. (The included angle is the angle in between the two sides.) Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 240.

  9. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 241.

  10. Write proof for Ex. 4 here: Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 241.

  11. Ex. 5. In the diagram, R is the center of the circle. If  SRT  URT, what can you conclude about triangle SRT and triangle URT ? The are congruent by the SAS Congruence Postulate. Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 241.

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