1. 9.5/10.3 CONGRUENT FIGURES VS. SIMILAR FIGURES ESSENTIAL QUESTIONS: 9.5 HOW CAN TRANSFORMATIONS BE USED TO VERIFY THAT TWO FIGURES HAVE THE SAME SHAPE AND SIZE? 10.3 – WHAT IS THE CONNECTION BETWEEN TRANSFORMATIONS AND THE ORIENTATIONS OF SIMILAR FIGURES? If two figures are similar, then there exists a sequence of translations, reflections, rotations, and/or dilations that transforms one figure into another. If two figures have the same shape and size, then there exists a sequence of translations, reflections, and/or rotations that transforms one figure into another.

2. RECALL… The lines ______ and ________of pre-images and images have the same ________ and measure under a translation, reflection and rotation. Two figures are considered __________ if one can be obtained by either a translation, reflection, or rotation. Congruent figures have the same __________________ If you are told that two figures are congruent, there must be a ____________(order that the transformation occurred) of translations, rotations, and reflections that took place. sides angles lengths congruent size and shape sequence

3. PROPERTIES OF CONGRUENCY If a shape is __________, then the shapes are no longer __________. It changes the __________of the shape, which means the new image is no longer congruent to the pre-image. Since not all figures are congruent, you need to ______the sequence of translations, reflections and rotations that occurred. dilated length congruent prove

4. HOW TO FIND THE SEQUENCE Ask yourself … ? Did the orientation change? Did the _______ change? If so, HOW? Did a ________ occur? If so, HOW? How about a _________? If so, HOW? To identify sequence …. use the ___________________ we learned about and put the sequence of events in the order it occurred. position rotation reflection coordinate notation

5. PROPERTIES OF SIMILARITY Two figures are _________ if one can be obtained from the other by a sequence of translations, reflections, rotations, and __________. Similar figures have the same _________, but may be different __________. Similar figures can be _________ where congruent figures ________. similar dilations shape sizes dilated cannot

6. Type of Transformation p SizeShape Orientation (direction) Position ReflectionNever AlwaysSometimes RotationNever AlwaysSometimes TranslationNever Always Enlargement (Dilation) AlwaysNever Sometimes Reduction (Dilation)AlwaysNever Sometimes