Download 02-21-17 Congruent Figures Notes

3/7/2017
Prebell
Congruent Figures
• Congruent (≅) Figures – have the same size
and shape; corresponding angles and sides
have equal measures
WB p. 187 # 5
– Corresponding Angles – angles that match
– Corresponding Sides – sides that match
The figures are congruent.
• Identify corresponding sides and angles.
Tell whether the two figures are
congruent. Explain your reasoning.
1. Answer the question
2. What do you know
about the topic?
3. Connect what you
know to the problem.
The figures are congruent.
a. What is the length of
side CD?
b. Which angle of KLMN
corresponds to ∠𝐵?
c. What is the perimeter
of ABCD?
The fronts of the houses are identical.
WB p. 24
a) What is the length of side 𝐿𝑀?
b) Which angle of 𝐽𝐾𝐿𝑀𝑁 corresponds to ∠𝐷?
c) Side 𝐴𝐵 is congruent to side 𝐴𝐸. What is the length of side 𝐴𝐵?
d) What is the perimeter of 𝐴𝐵𝐶𝐷𝐸?
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3/7/2017
Rigid Transformations
Sequence of Transformations
• Are used to prove congruency:
– Translations (direction and number of units)
• (𝑥, 𝑦) → (𝑥 + 𝑎, 𝑦 + 𝑏)
– Reflections (line of reflection)
• Across 𝑦 – axis: (𝑥, 𝑦) → (−𝑥, 𝑦)
• Across 𝑥 – axis: (𝑥, 𝑦) → (𝑥, −𝑦)
– Rotations (direction and angle of rotation)
• 90° CCW: 𝑥, 𝑦 → −𝑦, 𝑥
• 180°: (𝑥, 𝑦) → (−𝑥, −𝑦)
• 90° CW: (𝑥, 𝑦) → (𝑦, −𝑥)
Two figures are congruent if one can be
obtained from the other by a sequence of
translations, reflections, and rotations.
Identify a sequence of transformations that
will transform figure 𝐴 into figure 𝐵.
• Which transformation(s) change the
orientation of figures?
• Which do not?
• Two figures have the same size and shape.
What does this indicate about the figures?
Identify a sequence of transformations that
will transform figure 𝐵 into figure 𝐶.
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