Find the midpoint

1. Average! Find the midpoint -2 + 5 = 3 = 1 ½ 2 2 9 + -1 = 8 = 4 2 2 (9, -2) (-1, 5) (4,1.5)

2. Average! Find the midpoint 52 + 44 = 96 = 48 2 2 -17 + 13 = -4 = -2 2 2 (-17, 52) (13, 44) (-2,48)

3. Set up a proof—Do not prove! A Given: ΔABC is equilateral AH, BG, & CF are altitudes Prove: AH = BG = CF G F The altitudes of an equilateral triangle are congruent. C B H

4. Average! Find the midpoint 8 + 12 = 20 = 10 2 2 5 + -2 = 3 = 1.5 2 2 (5, 8) (-2, 12) (1.5,10)

5. Set up a proof—Do not prove! A Given: ΔABC is isosceles with base BC BG, & CF are medians Prove: BG = CF G F The medians to the legs of an isosceles triangle are congruent. C B

6. Set up a proof—Do not prove! A Given: ΔABC is isosceles with base BC BG, & CF are altitudes Prove: BG = CF G F The altitudes to the legs of an isosceles triangle are congruent. C B

7. Set up a proof—Do not prove! A Given: ΔABC is isosceles with base BC F is the midpoint of BC Prove: AF perpendicular to BC The line drawn from the vertex angle of an isosceles triangle to the midpoint of base is perpendicular to the base. C B F

8. 8 1 List all pairs of: 2. 7 2 6 3 5 4 a) 7 & 3; 2 & 6 a) Alt int b) 8 & 5; 1 & 4 b) corresponding c) 8 & 4; 1 & 5 c) Alt ext BACK

9. List all pairs of: 1 2 3 4 8 7 6 5 2 & 6, 7 & 3 Alt int angles Corresponding angles 2 & 4, 7 & 5, 8 & 6, 1 & 3 Interior angles on the same side of the transversal 2 & 3, 7 & 6 Alt ext angles 1 & 5, 8 & 4

10. List all pairs of: 1 2 3 4 8 7 6 5 1 & 7, 8 & 2, 3 & 5, 6 & 4 Vertical angles Corresponding angles 2 & 4, 7 & 5, 8 & 6, 1 & 3 Exterior angles on the same side of the transversal 1 & 4, 8 & 5