Transformations and Congruence
Transformations and congruence are fundamental concepts in the study of geometry, playing a crucial role in understanding the relationships between shapes and their properties. Transformations encompass a range of operations such as translations, rotations, reflections, and dilations, which alter the position, orientation, or size of geometric figures. Congruence, on the other hand, refers to the relationship between two figures that have the same size and shape. Together, transformations and congruence form the basis for exploring symmetry, similarity, and geometric relationships, providing a framework for solving problems in various mathematical contexts.
Questions
- Are two congruent polygons always similar?
- How do you find the image of A(4,-2) after it is reflected over the line y=2, then reflected over the line x=2?
- If three parts (angles and/or sides) of a triangle are congruent to that of another triangle, are the triangles congruent?
- If two sides of a triangle are congruent, then are the angles opposite those sides always, sometimes or never congruent?
- Rhombus WXYZ with vertices W(-4, 3), X(-1 1), Y(2,3), and Z(-1, 5) translated 2 units right and 5 units down. What are the new coordinates?
- When are similar figures congruent?
- Are the diagonals of a rectangle always, sometimes or never congruent?
- What special marks are used to show that segments are congruent?
- How do you rotate the figure B(-2,0), C(-4,3), Z(-3,4), and X(-1,4) 90 degree clockwise about the origin?
- On the coordinate plane, ΔABC ≅ ΔDEF by SSS. ΔABC translates 2 units to the left and 3 units down. Do the triangles remain congruent? Explain why or why not.