Chapter 4.2 Notes: Apply Congruence and Triangles

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Chapter 4.2 Notes Apply Congruence and Triangles

• Goal You will identify congruent figures.

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• Two geometric figures are congruent if they have
  exactly the same size and shape.
• Congruence Statements
• In two congruent figures, all the parts of one
  figure are congruent to the corresponding parts
  of the other figure.
• In congruent polygons, this means that the
  corresponding sides and the corresponding angles
  are congruent.

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• When you write a congruence statement for two
  polygons, always list the corresponding vertices
  in the same order.
• Congruence Statement __________________
• Corresponding angles ___________________
• Corresponding sides ____________________

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• Ex.1 Write a congruence statement for the
  triangles. Identify all pairs of congruent
  corresponding parts.

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• Ex.2 In the diagram, .
• a. Find the value of x.
• b. Find the value of y.

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• Ex.3 In the diagram below,
  .
• a. Identify all pairs of congruent
  corresponding parts.
• b. Find the value of x and find .

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• Ex.4 Show that .
• Theorem 4.3 Third Angles Theorem
• If two angles of one triangle are congruent to
  two angles of another triangle, then the third
  angles are also congruent.

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• Ex.5 Find .
• Ex.6 In the diagram, what is ?

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• Ex.7 The two triangles are congruent. Identify
  all angles and sides that are congruent. Then
  write a congruence statement.

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• Ex.8 In the diagram,
• a. Find the value of x.
• b. Find the value of y.

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• Properties of Congruent Triangles
• Theorem 4.4 Properties of Congruent Triangles
• Reflexive Property of Congruent Triangles For
  any triangle ABC, .
• Symmetric Property of Congruent Triangles
• If , then
  .
• Transitive Property of Congruent Triangles
• If
  , then
• .