This dynamic worksheet will help you understand how to interpret a geometric diagram.

1) Which angles look like right angles? 2) Which pairs of lines look like parallel lines? 3) Which angles look congruent? 4) Which segments look congruent? 5) Click the “Show Angle Measures” box. Drag the points of the angles around. • Which angle is actually a right angle? • Which angles are actually congruent? 6) Use the measure “Distance or Length” tool. Click on the segments. Drag the endpoints of the segments around. Which segments are actually congruent? 7) Drag the points on the lines around. Which lines are actually parallel? 8) Can you assume angles are right angles just because they look like it? __________ 9) Can you assume angles are congruent just because they look like it? _________ 10) Can you assume segments are congruent just because they look like it? _________ 11) Can you assume lines are parallel just because they look like it? _________

Perpendicular Bisectors

Part 1 1. Line CD is a perpendicular bisector of segment AB . Drag points A and B. Write a definition of perpendicular bisector based on your observations. 2. Click on: Show segments to the end points of segment AC. Drag point C. What can you say about any point on the perpendicular bisector? Part 2 3. Click on: Show triangle. 4. Click on: Show 2nd perpendicular bisector. 5. If F is on the perpendicular bisector of EB, what points are F equidistant from? 6. Click on: Show congruent segments. Part 3 7. Click on Show 3rd Perpendicular Bisector. What do you notice about the 3 perpendicular bisectors (red lines)? 8. Drag points A, B and E. Does your observation from #7 remain true? 9. Where is the intersection of the perpendicular bisectors of an acute triangle? right triangle? obtuse triangle? 10. Drag points C and F onto the intersection of the 3 perpendicular bisectors. What do you observe about the segments from the intersection to the vertices of the triangle (dotted lines)? Write a conclusion about this lab.

This is an interactive activity to learn about dilations.

1) Click on Dilation with “Center (0, 0).” Use the slider to adjust the “k” value. In your own words, describe dilation. 2) The scale factor is the ratio of a side length of the image to the corresponding side length of the pre-image. Scale Factor = . “k” is the scale factor of the dilation. Describe which k-values make the dilation an enlargement and which scale factors make the dilation a reduction. 3) Move the k-value to be 2. a. How does the coordinate of A’ compare to A? And B’ compare to B? And C’ to C? b. What happens to the image coordinates when the k-value is 3? 4) With the k-value on 2, click on “Show Segment Lengths.” a. How does A’B’ compare to AB? How does A’C’ compare to AC? And how does B’C’ compare to BC? b. How do the segment lengths compare when the k-value is 3? 5) Click on “Lines Through (0, 0) and A, B and C. What is the relationship between the pre-image points, the image points, the center of dilation, and these lines? (Hint: Try dragging the pre-image points to see how the image and lines move. Then adjust the scale factor to see how the image moves.) 6) Uncheck every box, then click on “Dilation with Center E” and “Show Segment Lengths.” You can click and drag point E around. Describe how the placement of the center of dilation affects the transformation. 7) Click on “Show Slopes.” How do the slopes of the segments of the pre-image compare to the slopes of the segments of the image? (You can drag points A, B and C around to see if your hypothesis is true.) 8) Uncheck every box. Click on “Composition 1.” First semester we talked about the transformations: reflection, rotation and translation. Recall that a composition is a combination of transformations. Dilation is a 4th kind of transformation. a. Which points of the image correspond to the pre-image? (Hint: Drag points A, B and C to find which points correspond to them.) b. Describe two transformations that make up Composition 1. 9) Uncheck every box. Click on “Composition 2.” Describe the two transformations that make up Composition 2.