Download 5.1: Corresponding Parts of Congruent Figures Brinkman

5.1: Corresponding Parts of Congruent Figures
Brinkman
SKILLS TO AQUIRE
 Identify and determine measures of parts of congruent figures.
 Make and justify conclusions about congruent figures.
1.) WHAT DOES IT MEAN TO BE CONGRUENT? Two shapes are congruent if they have the
same size and shape!
xo
C’
C
C’’
A”’
A
A’
A”
B”’
B
B’
B”
C”’
2.) What is happening in the diagram above from pre-image triangle ABC to triangle A”’B”’C”’?
A.) Translated from ABC to A'B'C'
B.) Reflection from A'B'C' to A"B"C"
C.) Rotated from A"B"C" to A"'B"'C"'
3.) Name 4 angles above that are congruent!
A
4.) Name 4 segments above that are congruent!
AB
A’
A’B’
A”
A”’
A”B”
A’”B”’
5.) Ultimately we can conclude that… triangles ABC and A”’B’”C’” are congruent! Sweet…
6.) Definition: Angles and sides that are images of each other under a transformation are called
CORRESPONDING PARTS
7.) Label the corresponding parts of congruency in the transformation diagram above!
8.) Definition: CPCF – CORRESPONDING PARTS OF CONGRUENT FIGURES Theorem
If two figures are congruent, then any pair of corresponding parts is congruent.
**Unless stated, corresponding parts of a figure refer to sides or angles.
9.) With a pair of congruent triangles, there are 6 PAIRS of corresponding parts:
3 PAIRS OF CONGRUENT ANGLES and 3 PAIRS OF CONGRUENT SIDES
10.)The order of VERTICES tells you which points are images of each other, and therefore,
which points CORRESPONDS
11.) HOWEVER! There may be other corresponding parts in a pair of congruent figures such as…
DIAGONALS and ANGLE BISECTORS
12.) REVIEW: By the REFLECTION POSTULATE: Every reflection preserves…
A) ANGLE MEASUREMENT
B) BETWEENNESS
C) COLLINEARITY
D) DISTANCE
13.) Definition: A-B-C-D Theorem: Every isometry preserves ANGLE MEASURE,
BETWEENNESS, COLLINEARITY AND DISTANCE.
Example: Suppose ABCD  WXYZ
C
Y
Z
X
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B
W
A
D
1.) What angle has measure equal to DAB ?
2.) Which segment has length equal to BD? (not drawn in picture) XZ
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3.) Which segment has equal length to CD? YZ
4.) Which angle has measure equal to WXY ?
5.) Which segment has equal length to AC? (not drawn in picture) WY
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