Translations geometry yx4/14/2024 ![]() ∠Y is common, then ∠XYB≅∠ZYA (additional information that is needed).b) What additional information would be necessary to prove that the two triangles, △XBY and △ZAY, are congruent? What congruency theorem would be applied? Answer Given: ∠X ≅ ∠Z □□ ≅ □□ Prove: □□ ≅ □□ a) Re-draw the diagram of the overlapping triangles so that the two triangles are separated. Use the diagram and given information to answer the questions and prove the statement. Prove that the triangles are congruent using a two-column proof and triangle congruency theorems. However, this congruency can also be proven using geometric postulates, theorems, and definitions. The congruency of △MNO and △XYZ can be proven using a reflection across the line bisecting □□. ANSWER CB // ED and both of BD and CE are transversals The point E will be the image of point C by rotation 180° around point F And The point D will be the image of point B by rotation 180° around point F Rotation is a kind of transformation So, ΔEDF will be the image of ΔCBF So, ΔCBF ≅ ΔEDF Part 2: Use congruency theorems to prove congruency. Be sure to name specific sides or angles used in the transformation and any congruency statements. Outline the necessary transformations to prove CBF ≅ EDF using a paragraph proof. Given: □□ ‖ □□ □□≅ □□ Prove: CBF ≅ EDF using isometric (rigid) transformations. Now, let’s get started! Part 1: Use transformations to prove congruency. You may be asked to upload the document, e-mail it to your teacher, or print it and hand in a hard copy. Your teacher will give you further directions about how to submit your work. You will be given partial credit based on the work you show and the completeness and accuracy of your explanations. Type all your work into this document, or print the document and show work by hand, so you can submit it to your teacher for a grade. So, be sure to show all your work and answer each question as you complete the tasks. In addition to the answers you determine, you will be graded based on the work you show, or your solution process. Otherwise, print this activity sheet and write your answers by hand. If your word processing program has an equation editor, you can insert your equations here. Be sure that all graphs or screenshots include appropriate information such as titles, labeled diagrams, etc. ![]() ![]() Be sure to show all work where indicated, including inserting images of graphs. Directions Complete each of the following tasks, reading the directions carefully as you go. ![]() Translation Reflection Rotation As you complete the task, keep these questions in mind: How can rigid transformations be used to prove congruency? How can congruency theorems be used to prove congruency? In this task, you will apply what you have learned in this unit to answer these questions. Many geometric proofs involve congruency statements, to be proven using isometric transformations or congruency theorems. This form of reasoning is the backbone for geometric proofs, utilizing definitions, postulates, theorems, and other properties of geometric figures to show that a statement is true. ![]() Geometric Proofs Logical, deductive reasoning requires a systematic way of thinking that outlines steps of mathematical statements to take given information and prove a mathematical statement. ![]()
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