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Geometry. Lesson 4 – 7 Congruence Transformations. Objective: Identify reflections, translations, and rotations. Verify congruence after a congruence transformation. Transformations. Transformations – An operation that maps an original figure ( preimage ) onto a new figure ( image ).

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Presentation Transcript
geometry

Geometry

Lesson 4 – 7

Congruence Transformations

Objective:

Identify reflections, translations, and rotations.

Verify congruence after a congruence transformation.

transformations
Transformations
  • Transformations –
    • An operation that maps an original figure (preimage) onto a new figure (image).
congruence transformations
Congruence Transformations
  • AKA rigid transformations
  • AKA isometric (isometry)
  • The position of the image may differ from that of the preimage, but the two figures remain congruent.
types of congruence transformations
Types of Congruence Transformations
  • Reflection
    • A transformation over a line called the line of reflection. A flip over a line.
types of congruence transformations1
Types of Congruence Transformations
  • Translation
    • A transformation that moves all points of the original figure the same distance in the same direction. A slide of the points
types of congruence transformations2
Types of Congruence Transformations
  • Rotation
    • A transformation around a fixed point called the center of rotation. Each point of the original figure and it image are the same distance from the center. A turn about a point.
identify the type of congruence transformation shown as a reflection translation or rotation
Identify the type of congruence transformation shown as a reflection, translation, or rotation.

Rotation

Reflection

Translation

identify the type of congruence transformation shown as a reflection translation or rotation1
Identify the type of congruence transformation shown as a reflection, translation, or rotation.

Translation

Rotation

Reflection

slide9
Identify the type of congruence transformation shown in the diagram as a reflection, translation, or rotation.

Rotation

slide10
Identify the type of congruence transformation shown in the diagram as a reflection, translation, or rotation.

Translation

Reflection

verify congruence after transformation
Verify Congruence after Transformation
  • Triangle XZY with vertices X (2, -8), Z (6, -7), and Y(4, -2) is a transformation of Triangle ABC with vertices A (2, 8), B (6, 7), and C (4, 2). Graph the original figure and its image. Identify the transformation and verify that it is a congruence transformation.

Reflection

Cont…

verify the triangles are congruent
Verify the triangles are congruent
  • Since no angles are known we will prove congruence by SSS.
homework
Homework
  • Pg. 297 1 – 6 all, 8 – 28 E, 32, 38 – 42 E, 46 – 50 E
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