congruent triangles
DESCRIPTION
CONGRUENT TRIANGLES . How To Find Congruent Sides ? ?. Remember to look for the following:. Adjacent triangles share a COMMON SIDE , so you can apply the REFLEXIVE Property to get a pair of congruent sides . - PowerPoint PPT PresentationTRANSCRIPT
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CONGRUENT
TRIANGLE
S
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HOW TO FIND CONGRUENT SIDES ? ?Remember to look for the following:
• Adjacent triangles share a COMMON SIDE, so you can apply the REFLEXIVE Property to get a pair of congruent sides.
• Look for SEGMENT BISECTORS.. They lead to MIDPOINTS…. Which lead to congruent segments.
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USE SSS TO EXPLAIN WHY ∆ABC ∆CDA.
AB CD and BC DA Given
AC CA Reflexive ∆ABC ∆CDA SSS
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An included angle is an angle formed by two adjacent sides of a polygon.
B is the included angle between
&AB BC
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HOW TO FIND CONGRUENT ANGLES ? ?Remember to look for the following:
• Look for VERTICAL ANGLES.
• Look for lines. They form adjacent angles.
• Look for // LINES CUT BY A TRANSVERSAL. They lead to ANGLES.
• Look for < BISECTORS. They lead to ANGLES.
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The letters SAS are written in that order because the congruent angles must be INCLUDED between pairs of congruent corresponding sides.
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Engineering ApplicationThe diagram shows part of the support structure for a tower. Use SAS to explain why ∆XYZ ∆VWZ.XZ VZ YZ WZ Given
XZY VZW VERTICAL <‘s are
∆XYZ ∆VWZ SAS .
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An included side is the common side of two consecutive angles in a polygon. The following postulate uses the idea of an included side.
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When using ASA , the side must be INCLUDED between the angles known to be congruent.
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Determine if you can use ASA to prove NKL LMN. Explain.
KL and NM are //.
KLN MNL, because // lines imply alt int >s. NL LN by the Reflexive Property.No other congruence relationships can be determined, so ASA cannot be applied.
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When using AAS , the sides must be NONINCLUDED and opposite corresponding angles.
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Use AAS to prove the triangles
Given: JL bisects KLM K MProve: JKL JML JL bisects KLM K M Given
JL JL ReflexiveKLJ MLJ Def. < bis.
JKL JML AAS
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When using HL , you must FIRST state that there is a RIGHT TRIANGLE!
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Determine if you can use the HL Congruence Theorem to prove ABC DCB.
AC DB Given
BC CB Reflexive ABC & DCB are right angles Given
ABC & DCB are rt. s Def. right ABC DCB HL.
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WAYS TO PROVE TRIANGLES
SSS SAS
AASASA
HL