Download Unit 5 Classification of Triangles

5.1 ­­ Congruence and Triangles
Unit 5
corresponding sides and angles
Classification of
Triangles
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Sides:
Angles:
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Figures are congruent if all pairs of corresponding angles are congruent and all pairs of corresponding sides are congruent!
C
P
N
M
E
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D
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X
K
W
U
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H
Y
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Q
R
S
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T
8
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1
A
B
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35
35
C
D
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Ticket­out­the­Door
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5.2 ­­ Proving Triangles are Congruent: SSS and SAS
Assignment: pages 236­237 #14­26, 34, 38, 40, 41, 42, 44
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Side­Side­Side Congruence Postulate (SSS)
If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.
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Side­Angle­Side Congruence Postulate (SAS)
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.
What is an included angle?
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Z
Y
X
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c.
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N
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Let's try a proof!
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L
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Maybe just one more...
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Ticket­out­the­Door
Assignment: pages 245­246 #10­26 even, 30, 34
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5.3 ­­ Proving Triangles are Congruent: ASA and AAS
Angle­Side­Angle Congruence Postulate (ASA)
If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.
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d.
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Angle­Angle­Side Congruence Theorem (AAS)
If two angles and a non­included side of one triangle are congruent to two angles and the corresponding non­included side of a second triangle, then the two triangles are congruent.
What additional congruence is needed to show that triangle QPS triangle QRS by the AAS Congruence Theorem?
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White Board Practice!!!
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5.4 ­­ Hypotenuse­Leg Congruence Theorem (HL)
If the hypotenuse and a leg of a RIGHT triangle are congruent to the hypotenuse and a leg of a second RIGHT triangle, then the two triangles are congruent.
Assignment: pages 254-255 #10-32 even
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Summary
SSS
SAS
Is it possible to show that triangle ABC is congruent to triangle ADC using the HL Congruence Theorem? Explain your reasoning.
ASA
A
AAS
D
B
HL
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You try:
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A
c.
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B
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E
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Ticket out the Door
Assignment: pages 260­262 #10, 12, 16, 18, 20, 22, 26, 30
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5.6 ­­ Angle Bisectors and Perpendicular Bisectors
How do you find distance from a point to a line?
5.1­5.4 review: page 683 #1­15
Equidistant
­when a point is the same distance from one line as it is from another line.
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Perpendicular Bisector Theorem
­If a point is on the perpendicular bisector of a segment,
then it is equidistant from the endpoints of the segment.
Angle Bisector Theorem
­If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
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Use the diagram to find AB.
G
Use the diagram to find GH.
3x+2
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H
5x­12
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Assignment: page 277 #10­12, 14­19
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5.7 ­­ Reflections Reflection
­a transformation that creates a mirror image
Properties of reflections:
1) The reflected image is congruent to the original figure.
2) The orientation of the reflected image is reversed.
3) The line of reflection is the perpendicular bisector of the segments joining the corresponding points.
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5.7 continued ­­ Symmetry
Assignments:
­ pages 286­287 #8­16, 18, 31, 34, 36
­ worksheet
­coloring page
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Symmetry of Shapes Activity
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Line of symmetry ­a line of reflection
How many lines of symmetry are in a square?
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What is a kaleidoscope?
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Assignments:
Test Review:
­ pages 287­288 #21­29, 34, 36, 37, 39
­ONE partner
­worksheet
­complete pages 683­684 #1­29 all
­finish reflection coloring page
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