This presentation illustrates various congruency rules in triangles. Useful for class vii to x
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Proving Triangles Congruent
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The Idea of a Congruence Two geometric figures with exactly the same size and shape.
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How much do you need to know... , about two triangles 000 to prove that they are congruent?
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Corresponding Parts In Lesson 4.2, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. AABC = A DEF
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Do you need all six ? NO ! SSS SAS ASA A AS
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Side-Side-Side (SSS) 2. BC 3. AC AABC DEF
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Side-Angie-Side (SAS) *AABC A DEF O included angle
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Included Angle The angle between two sides
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Y s Included Angle Name the included angle: YE and ES ES and Y S and YE
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Angle-Side-Angle (ASA) 2, AB DEO AABC = A DEF include
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Included Side between two angles The side HI
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Included Side Name the included angle: Y s ZY and ZE ZE and Z S LS and ZY YE ES SY
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Angle-Angie-Side (AAS) 2. z B AABC = A DEF O Non-included side
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Warning: No SSA Postulate There is no such thing as an SSA B postulate! c D NOT CONGRUENT
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Warning: No AAA Postulate There is no such thing as an AAA postulate! c NOT CONGRUENT
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The Congruence Postulates G-SSS correspondence ASA correspondence SAS correspondence AAS correspondence AAA c
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Name That Postulate SAS (when possible) ASA sss
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Name That Postulate (when possible) ASA RIY SAS
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Name That Postulate Reflexive SAS Property Vertical SAS Angles (when possible) Vertical Angles SAS Reflexive Property
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HW: Name That Postulate (when possible)
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HW: Name That Postulate (when possible)
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Let's Practice Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:
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Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:
Discussion
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