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Geometry Unit 3 Level 1 Questions Name______________________________ 3A- Know and apply vocabulary and theorems related to objects created by angles and lines 1. Draw a picture of two lines intersected by a transversal and correctly label a pair of corresponding angles. 2. Draw a picture of two lines intersected by a transversal and correctly label a pair of alternate interior angles. 3. Draw a picture of two lines intersected by a transversal and correctly label a pair of same side interior angles. 4. Draw a picture of two lines intersected by a transversal and correctly label a pair of alternate exterior angles. 5. Draw a picture of two lines intersected by a transversal and correctly label a pair of same side exterior angles. 6. Write out two theorems involving parallel lines and a transversal. Illustrate your theorem with a diagram. 7. What is the sum of the exterior angles of a convex polygon with n sides? 8. What is the sum of the interior angles of a convex polygon with n sides? 9. What is a median of a triangle? 10. What is an altitude of a triangle? 3C – Apply properties of equations of parallel and perpendicular lines to geometric figures 1. Write the slope intercept form for the equation of a line and explain all the variables. 2. Write the point slope form for the equation of a line and explain all the variables. 3. Find the equation of a line passing through the points 2,3 and 4, 6 . 4. Find the equation of a line with a slope of 3 and a y-intercept of 0, 6 . 5 5. Find the equation of the line parallel to the line y 3 x 3 and passing through the point 2,5 . 4 6. Find the equation of the line perpendicular to the line y 7. Find the intersection of the lines y 3 x 3 and passing through the point 0,5 . 4 3 3 x 3 and y x 6 . 4 2 3D – Apply midpoint, slope, and distance to justify conjectures about geometric figures. 1. Define midpoint of a segment. 2. Find the midpoint of the segment whose endpoints are 3, 4 and 21,15 . 3. The midpoint of a segment is 3, 2 . One of the endpoints is 13,6 . What is the other endpoint? 4. What is the distance formula? 5. Using the distance formula, find the length of AB for point A 1,3 and B (1, 6) . 6. How do we use slope to determine if two lines are parallel? 7. How do we use slope to determine if two lines are perpendicular? 3F - Analyze problem situations and apply definitions, postulates, theorems to solve. Use the picture at the right to answer the following questions. 1. If line a b , write out a theorem that b relates 1 and 5 . a 1 2 3 4 c d 14 13 15 16 2. Name a pair of corresponding angles. 3. Write out a theorem that would prove line a b if m2 m5 180o . 4. If m5 m10 , what theorem would guarantee that line c d ? 5 6 8 7 12 9 11 10 3G - Analyze problem situations and apply algebra to solve. Use the diagram provided to answer the following questions. Assume a b and c d . If m14 5x 10 and m9 88 2x , find x and m14 . b a 1 2 3 4 c d 14 13 15 16 If m7 3x 9 and m3 6x , find x and m3 . If m1 36 o and m3 18 x 6 y , and m16 6 x 10 y find x, y, and m3 . 5 6 8 7 12 9 11 10 3H - Prove conjectures related to lines and angles There are no genuine Level 1 questions about proof. What you can do to help is list the theorems that you know about angles. This would help. So for a Level 1 score, list four theorems you know about angles on parallel lines. List three theorems you know about the angles of convex polygons. (Yes, a triangle is a convex polygon.)