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Name: _________________________________ Date: __________________ Period: ______ Geometer’s Sketchpad Introduction to 3.2 Directions: 1. Draw a line and label the two points on the line A and B. Geometry w/ Trig E suur 2. Plot a point (label it C) not on AB . suur 3. Draw a line through point C parallel to AB . (This can be done by selecting C and AB . In the construct menu select “parallel line.”) G A B C H D 4. Plot a point on the new parallel line that contains point C. Label this point D. F 5. Draw a transversal line. Label the two points on the line E and F. 6. Construct the intersection of each parallel line with the transversal. (Highlight one parallel line and the transversal. In the construct menu, select “intersection.” Repeat for the second parallel line.) Label the intersections G and H. 7. Your sketch should look something like the above diagram. 8. Find the measure of all eight angles. (Select 3 points that form the angle, and select “angle” from measure menu – the vertex must be the second point you select.) Drag each measurement so that it is located inside the angle. 9. Name two pairs of alternate interior angles: ________________________________________________ 10. What do you notice about the angle measures of each pair of alternate interior angles? 11. Name two pairs of alternate exterior angles: _______________________________________________ 12. What do you notice about the angle measures of each pair of alternate exterior angles? 13. Name two pairs of corresponding angles: __________________________________________________ 14. What do you notice about the angle measures of each pair of corresponding angles? 15. Name two pairs of consecutive interior angles: ___________________________________________ 16. What do you notice about the angle measures of each pair of consecutive interior angles? 17. Move your transversal so that mAGE 90 . What do you notice about the measurement of CHG ? 18. Make some conjectures based on your Sketchpad Activity! Then use your new theorems/postulates to fill in all seven missing angle measures in the diagram. If two parallel lines are cut by a transversal, then each pair of… Corresponding angles are __________________________. Alternate interior angles are ________________________. Alternate exterior angles are _________________________. Consecutive interior angles are _______________________________. In a plane, if a line is perpendicular to one of two parallel lines, then ___________________________________________________________________________________. Get this paper checked by your teacher before continuing. 80° Practice: Solve for the variable. State the theorem or postulate that justifies your reasoning. 1. If 2 II lines are cut by a transversal, then ________________________________________ are _________________________________. (type of angles) (≅/supplementary) x = _______________ 2. To solve for x: If 2 II lines are cut by a t, then ________________________________________ are _______________________________. (type of angles) (≅/supplementary) To solve for y: If 2 II lines are cut by a t, then ________________________________________ are _______________________________. (type of angles) (≅/supplementary) 3. State TWO theorems/postulates used: x = _______________, y = _______________ If _________________________________________________________, then ______________________________________________________________. If _________________________________________________________, then ______________________________________________________________. y = _______________ 4. **Challenge! Solve for x, y, and z. x = _______________, y = ______________, z = ______________