4'2 Congruence and Triangles

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4.2 Congruence and Triangles

• Geometry
• Fall 2008

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Objectives

• To identify congruent figure and corresponding
  parts.
• To prove that two triangles are congruent.

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Congruent Figures
Two geometric figures that have exactly the same
size and shape.
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Congruent Figures

• When two figures are congruent, there is a
  correspondence between their angles and sides
  such that corresponding angles are congruent and
  corresponding sides are congruent.

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Congruent Figures
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Example 1

• Write a congruence statement.
• Identify all pairs of corresponding parts.

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Example 2

• In the diagram, NPLM EFGH.
• (a) Find the value of x.
• (b) Find the value of y.

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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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Example 3

• Find the value of x.

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Example 4

• Decide whether the triangles are congruent.
  Justify your reasoning.

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Theorem 4.4 Properties of Congruent Triangles

• Reflexive Property of Congruent Triangles
• Every triangle is congruent to itself.

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Theorem 4.4 Properties of Congruent Triangles

• Symmetric Property of Congruent Triangles

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Theorem 4.4 Properties of Congruent Triangles

• Transitive Property of Congruent Triangles