NAME _____________________________________________ DATE ____________________________ PERIOD _____________
4-7 Study Guide and Intervention
Congruence Transformations
Identify Congruence Transformations A congruence transformation is a transformation where the original figure,
or preimage, and the transformed figure, or image, figure are still congruent. The three types of congruence
transformations are reflection (or flip), translation (or slide), and rotation (or turn).
Example: Identify the type of congruence transformation shown as a reflection, translation, or rotation.
a.
b.
Each vertex and its image are the
same distance from the y–axis.
This is a reflection.
c.
Each vertex and its image are in
the same position, just two units
down. This is a translation.
Each vertex and its image are
the same distance from the
origin. The angles formed by
each pair of corresponding
points and the origin are
congruent. This is a rotation.
Exercises
Identify the type of congruence transformation shown as a reflection, translation, or rotation.
1.
2.
3.
4.
5.
6.
Chapter 4
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Glencoe Geometry
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
4-7 Study Guide and Intervention (continued)
Congruence Transformations
Verify Congruence You can verify that reflections, translations, and rotations of triangles produce congruent triangles
using SSS.
Example: Verify congruence after a transformation.
△WXY with vertices W(3, –7), X(6, –7), Y(6, –2) is a transformation of △RST with
vertices R(2, 0), S(5, 0), and T(5, 5). Graph the original figure and its image. Identify
the transformation and verify that it is a congruence transformation.
Graph each figure. Use the Distance Formula to show the sides are congruent and the
triangles are congruent by SSS.
RS = 3, ST = 5, TR = √(5 − 2)2 + (5 − 0)2 = √34
WX = 3, XY = 5, YW= √(6 − 3)2 + (− 2 − (−7))2 = √34
̅̅̅̅ ≅ 𝑊𝑋
̅̅̅̅ ≅ 𝑋𝑌
̅̅̅̅̅, 𝑆𝑇
̅̅̅̅, 𝑇𝑅
̅̅̅̅ ≅ 𝑌𝑊
̅̅̅̅̅
𝑅𝑆
By SSS, △RST ≅ △WXY.
Exercises
COORDINATE GEOMETRY Graph each pair of triangles with the given vertices. Then identify the
transformation, and verify that it is a congruence transformation.
1. A(−3, 1), B(−1, 1), C(−1, 4);
D(3, 1), E(1, 1), F(1, 4)
Chapter 4
2. Q(−3, 0), R(−2, 2), S(−1, 0);
T(2, −4), U(3, −2), V(4, −4)
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Glencoe Geometry