unit 2 day 5 congruence transformations mr. kugler frank h. peterson academies of technology
TRANSCRIPT
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UNIT 2 DAY 5CONGRUENCE
TRANSFORMATIONSMR. KUGLER
FRANK H. PETERSON ACADEMIES OF TECHNOLOGY
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MATCHING
1. Translation
2. Rotation
3. Reflection
A. This transformation creates points that are equidistant from a single point.
B. This transformation does not change orientation of the figure.
C. This transformation creates points that are equidistant from a line.
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Objective:• The student will be able to identify
congruence transformations.• Students will show mastery of
transformation concepts.
Essential Question:
• What do you need to show to prove that the triangles are congruent?
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KFC – KNOWLEDGE FOR COLLEGEDefinition:
A single or composition of rigid motions that moves a congruent geometric figure onto another one.
Characteristics and Tendencies:
The sides must be congruent and the angles must be congruent to know that the transformation is a perfect mapping onto the other.
Example:
(T<1, 5> ∘ r(90°, O))( ∆PQR) = ∆STU
Congruence Transformations
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IDENTIFYING CONGRUENCE TRANSFORMATIONS
Based on the naming rules of congruency, the name will always tell us which parts must be corresponding. It gives us our starting point.
Focusing on a set of corresponding sides is typically easier to figure out if a rotation OR reflection is needed. It is very rare that both would be used in a test question.
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MATCHING
1. Translation
2. Rotation
3. Reflection
4. Glide Reflection
A.
B.
C.
D.
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Find the coordinates of
the vertex M’.
Rx-axis(MATH)
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Find the coordinates of
the vertex H’.
T<–1, 2>(MATH)
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Find the coordinates of
the vertex A’.
r(90°, O)(MATH)
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Find the coordinates of
the vertex T’.
(Ry-axis ○ T<0, 2>)(MATH)
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• The point (1, 1) is the image under the translationT<5, 5> (x, y). What is its preimage?
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The point (a, b) is rotated about the origin -90° and then reflected in the y-axis. Which pair of coordinates best describes the resulting transformation of the point?
(a, -b), (b, -a), (b, a), (-b, -a), (-a, -b), (-a, b), (-b, a)
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The point (a, b) is rotated about the origin 180° and then reflected in the y-axis. Which pair of coordinates best describes the resulting transformation of the point?
(a, -b), (b, -a), (b, a), (-b, -a), (-a, -b), (-a, b), (-b, a)
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•Write down all of the Rigid Motions.
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Write down the Congruency
Transformation.
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Write down the Congruency
Transformation.
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•Point R(x, y) moves 13 units West and 14 units South. What is a rule thatdescribes this translation?
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What is the degree measurement after a Clockwise rotations around point O from point B to C?
O
A
H
G
F E
D
C
B
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What is the degree measurement after a Counter-Clockwise rotations around point O from point C to H?
O
A
H
G
F E
D
C
B
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What is the degree measurement after a Clockwise rotations around point O from point A to G?
O
A
H
G
F E
D
C
B
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What is the degree measurement after a Counter-Clockwise rotations around point O from point B to C?
O
A
H
G
F E
D
C
B
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•What is the image of (6, 6) after a reflection across the y-axis?
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Write a single transformation rule that has the same effect as the composition of transformation listed below.
T<–3, 4> ○ T<1, –2>
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Write a single transformation rule that has the same effect as the composition of transformation listed below.
Ry = –2 ○ Ry = 2
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Write a single transformation rule that has the same effect as the composition of transformation listed below.
Rx = 1 ○ Ry = –1
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HOME LEARNINGTonight
• Make sure I have your Construction Portfolio Review
Over the Weekend• Review all of the notes and home learning• Re-watch the videos on Pearson Realize
• Make Flashcards to memorize the Rotation Rules