Transformations and Congruence Test 2 Review
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1 Transformations and Congruence Test 2 Review 1.To understand the different transformations: Be able to define and understand transformations (rotation, reflection, dilation, translation, glide reflection, isometry, etc.) 2. Be able to perform transformations: Given a preimage, one should be able to produce the image given a transformation or transformation rule 3. Derive and use transformation rules: Students should be able to derive the transformation rules and apply these rules to transformations. Be able to take a point and transform it multiple times using transformation rules. 4. Explain how transformations and congruency are related: Use transformations as a way to prove or disprove that triangles are congruent. 5. Explain the triangle congruency theorems and postulates: Be able to explain why AAA and ASS do not work. 6. State whether triangles are congruent or if there is Not Enough Information (NEI): Given two triangles, state whether the two triangles are congruent using SSS, SAS, etc. or NEI using AAA or ASS. Students must be able to use Reflexive Property and Vertical angles in their explanations. 7. Symmetry and order: Find the line of symmetry or minimal rotation of figures. Find the order of figures. NEED HELP? Let me know!!
2 To understand the different transformations 1. Name all of the transformations. 2. Are the following isometries? 3. Explain the difference between a translation and a transformation. 4. Which transformation is being described by the following definition: A transformation that turns a figure about a fixed point
3 5. Identify the following transformations. Be able to perform transformations 6. Draw the figure with coordinates A(1, 2), B (3, 5) and C (7, 2). Reflect this over the x-axis and draw the image.
4 7. Draw the figure with coordinates A(1, 2), B (3, 8) and C (6, 2 ). Apply the rule (x, y) à ( x 5, y - 2) and draw the image. 8. Draw the figure with coordinates A(-2, -2), B (2, -2) and C (1, 2). Dilate this figure by a scale factor of 3.
5 9. Draw the figure with coordinates A(-2, 2), B (-5, 5) and C (-4, 8). Reflect this over the line y = x 10. Draw the figure with coordinates A(2, 2), B (5, 5) and C (4, 8). Rotate this triangle 90 degrees clockwise
6 Derive and use transformation rules 11. Use the picture below to derive the rule for reflecting over the line y = x. DO NOT LOOK AT YOUR NOTES 12. Use the picture below to derive the rule for rotating a figure 180 degrees counter clockwise. DO NOT LOOK AT YOUR NOTES
7 13. Come up with the following transformation rules. Grab a whiteboard to help you, but do NOT use your notes. You must be able to explain how you derived these rules on your test tomorrow. 14. Perform the following transformations on the point given below. Use transformation rules A ( 1, 2) Reflect A over the x-axis. This gives A (, ) Rotate A 270 degrees clockwise. This gives A (, ) Translate A using the rule (x,y)à (x + 4, y 2). This gives A (, )
8 15. Perform the following transformations on the point given below. Use transformation rules A ( -5, 2) Reflect A over the y-axis. This gives A (, ) Rotate A 90 degrees clockwise. This gives A (, ) Dilate A using a scale factor of 2. This gives A (, ) Explain how transformations and congruency are related 16. Explain why the two triangles below are congruent using transformations. In other words, show how triangle ABC maps onto triangle PQR.
9 Explain the triangle congruency theorems and postulates 17. Explain why AAA is NOT enough information to prove triangles congruent. Give an example. 18. Name the congruency postulates that DO work: State whether triangles are congruent or if there is Not Enough Information (NEI) Directions: State whether the two triangles are congruent and how you know. If there is not enough information, state NEI
10 Directions: State whether the two triangles are congruent and how you know. If there is not enough information, state NEI 20. Write three TRIANLGE congruency statements for the triangles below:
11 21. Given that the two triangles are congruent below, name the six facts we know to be true Symmetry and order 22. State the order and minimal rotation of each image
12 23. Draw the lines of symmetry in the figures below
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