Math 2 Geometry Based on Elementary Geometry, 3rd ed, by Alexander

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Math 2 GeometryBased on Elementary Geometry,
3rd ed, by Alexander Koeberlein

• 3.2
• Corresponding Parts of Congruent Triangles

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CPCTC

• Corresponding parts of congruent triangles are
  congruent.
• We first need to prove two triangles are ?
• Could possibly use SSS, SAS, ASA, AAS

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Example 1

• Given
• Ray WZ bisects ?TWV
• Seg WT ? Seg WV
• Prove
• Seg TZ ? Seg VZ

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Example 1a

• Given
• Ray WZ bisects ?TWV
• Seg WT ? Seg WV
• Prove
• Seg WZ bisects Seg TV

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Three types of ? conclusions

• Proving triangles congruent
• Proving the congruence of corresponding parts of
  triangles. First need to prove the triangles are
  congruent.
• Establishing further relationships like in
  previous example. Need to first establish two
  triangles are congruent.

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Example 2

• Given
• Seg ZW ? Seg YX
• Seg ZY ? Seg WX
• Prove
• Seg ZY Seg WX

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Right Triangles
Hypotenuse
Leg
Leg
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HL (Hypotenuse-Leg)Theorem 3.2.1

• Method for Proving Triangles Congruent
• If the hypotenuse and a leg of one right triangle
  are congruent to the hypotenuse and leg of a
  second triangle, then the triangles are congruent.

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Example

1. SegAB ? SegEC and SegAC ? Seg ED
2. ?A ? ?E and C is midpoint of SegBD
3. SegBC ? SegCD and ?1 ? ?2
4. SegAB ? SegEC and SegEC bisects SegBD

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Example

1. SegAB ? SegEC and SegAC ? Seg ED
2. ?A ? ?E and C is midpoint of SegBD
3. SegBC ? SegCD and ?1 ? ?2
4. SegAB ? SegEC and SegEC bisects SegBD

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ExampleCite reason why rt ?ABC ? rt ?ECD

1. SegAB ? SegEC and SegAC ? Seg ED

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Example

1. SegAB ? SegEC and SegAC ? Seg ED
2. ?A ? ?E and C is midpoint of SegBD

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Example

1. SegAB ? SegEC and SegAC ? Seg ED
2. ?A ? ?E and C is midpoint of SegBD
3. SegBC ? SegCD and ?1 ? ?2

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Example

1. SegAB ? SegEC and SegAC ? Seg ED
2. ?A ? ?E and C is midpoint of SegBD
3. SegBC ? SegCD and ?1 ? ?2
4. SegAB ? SegEC and SegEC bisects SegBD

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Pythagorean Theorem

• The square of the length (c) of the hypotenuse
  of a right triangle equals the sum of the square
  of the lengths (a and b) of the legs of the
  triangle

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Square Roots Property

• Let x represent the length of a line segment,
  and let p represent a positive number. Then,
• Note Different from Square Roots Property in
  Algebra

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ExampleFind the length of the third side of the ?

1. Find c if a 6 and b 8.

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ExampleFind the length of the third side of the ?

1. Find c if a 6 and b 8.
2. Find b if a 7 and c 10