A student was asked to construct a line through point that is perpendicular to . C She constructed a circle with center passing through and labeled the other point C A where the circle intersects as point D. Then she constructed two more circles, one with center passing through and the A D other with center passing through She labeled one of the points where those circles D A. intersect as point E. Finally she drew segments , , and . Prove that (Optional Hint: Use the SSS Congruence Theorem.) ∆ACE ∆DCE. because ___________________________________________ is a straight angle since its sides lie on one line. Use this fact to explain why ⃡ How would you find the midpoint of a segment if the only tools you had were a compass and straightedge? (No marked ruler!) You may use the segment below to demonstrate. Write proofs for each of these exercises: a. Given: is the midpoint of both and Prove: C ∆ACE ∆BCD b. With the same diagram and given in part (a), now prove that || . (draws on Unit 3)
A student was asked to construct a line through point C that is perpendicular to . She constructed a circle with center C passing through A and labeled the other point where the circle intersects as point D. Then she constructed two more circles, one with center A passing through D and the other with center D passing through A. She labeled one of the points where those circles intersect as point E. Finally she drew segments , , and . Prove that ∆ACE ∆DCE. (Optional Hint: Use the SSS Congruence Theorem.) because ___________________________________________ is a straight angle since its sides lie on one line. Use this fact to explain why ⃡ How would you find the midpoint of a segment if the only tools you had were a compass and straightedge? (No marked ruler!) You may use the segment below to demonstrate. Write proofs for each of these exercises: a. Given: C is the midpoint of both and Prove: ∆ACE ∆BCD b. With the same diagram and given in part (a), now prove that || . (draws on Unit 3)
Geometry_Midterm_Questions.docx