1. 4-1 Detour Proofs Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. Advanced Geometry

2. Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. A B C D E F G Warm-Up Given: Prove: STATEMENTS REASONS

3. Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. The Midpoint Formula If A = and B =, then the midpoint M = of can be found by using the midpoint formula: A B M

4. Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. Note the difference between Slope and Midpoint: Slope is the ratio of rise to run. Thus the answer to a slope question is a ratio (fraction). Slope is calculated using the formula: The Midpoint is a Point. Thus the answer to a Midpoint question is an ordered pair that gives the x and y coordinates of that point. The x coordinate of the midpoint is the AVERAGE of the x coordinates of the segment's endpoints and the y coordinate of the midpoint is the AVERAGE of the y coordinates of the segment's endpoints.

5. Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. Example: Find the Slope and the Midpoint of the segment having endpoints at (-4, 1) and (8, 7). Slope Midpoint

6. Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.

13. STATEMENTS REASONS

14. Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.

17. Assignment 4.1: 1-9

18. Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.

19. STATEMENTS REASONS

20. Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. STATEMENTS REASONS

21. Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent.

26. STATEMENTS REASONS

27. Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. STATEMENTS REASONS

28. Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. STATEMENTS REASONS

29. Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. STATEMENTS REASONS

30. Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. STATEMENTS REASONS

31. Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. STATEMENTS REASONS

32. Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. STATEMENTS REASONS

33. Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. STATEMENTS REASONS

34. Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. STATEMENTS REASONS

35. Learner Objective: I will calculate midpoints of segments and complete proofs requiring that more than one pair of triangles be shown congruent. STATEMENTS REASONS