Lesson 4 – 7 Congruence Transformations

GeometryLesson 4 – 7

Congruence Transformations

Objective:Identify reflections, translations, and rotations.

Verify congruence after a congruence transformation.

TransformationsTransformations – An operation that maps an original figure

(preimage) onto a new figure (image).

Congruence Transformations

AKA rigid transformationsAKA isometric (isometry)

The position of the image may differ from that of the preimage, but the two figures remain congruent.

Types of Congruence Transformations

ReflectionA transformation over a line called the line of

reflection. A flip over a line.

Types of Congruence TransformationsTranslationA transformation that moves all points of the

original figure the same distance in the same direction. A slide of the points

Types of Congruence TransformationsRotationA 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.

Rotation Reflection Translation

Identify the type of congruence transformation shown as a reflection,

translation, or rotation.

Reflection Rotation Translation

Identify the type of congruence transformation shown in the diagram as a reflection, translation,

or rotation.

Rotation

Identify the type of congruence transformation shown in the diagram as a reflection, translation,

or rotation.

Translation Reflection

Verify Congruence after TransformationTriangle 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 congruentSince no angles are known we will prove congruence by SSS.

178726 22 AB

292746 22 BC 102408224 22 AC 17)8(726 22 XZ 29)2(746 22 ZY

10240)2(842 22 XY

SSSbyXZYABC

HomeworkPg. 297 1 – 6 all, 8 – 28 E, 32, 38 – 42 E, 46 – 50 E