Given: ΔABC
Prove: The medians of ΔABC are concurrent.
Proof:
Statements Reasons<...
Mathematics, 02.06.2021 21:00, debiruuu
Given: ΔABC
Prove: The medians of ΔABC are concurrent.
Proof:
Statements Reasons
1. The vertices of ΔABC are unique points: A(x1,y1), B(x2,y2), and C(x3,y3). Given
2. Use rigid transformations to transform ΔABC into ΔA'B'C', so that vertex A' is at the origin and A'C' lies on the x-axis in the positive direction. In the coordinate plane, any point can be moved to any other point using rigid transformations and any line can be moved to any other line using rigid transformations.
3. Any property that is true for ΔA'B'C' will also be true for ΔABC. Definition of congruence
4. Let r, s, and t be real numbers such that the vertices of ΔA'B'C' are A'(0,0), B'(2r,2s), and C'(2t,0). Defining constants
5. Let D', E', and F' be the midpoints of A'B', B'C', and A'C' respectively. Defining points
6. D' = (r , s)
E' = (r + t, s)
F' = (t, 0) Definition of midpoints
7. Slopes of lines:
Definition of slope
8. Equations of lines:
Using point-slope formula
9. Lines A'E' and B'F' intersect at point P.
Algebra
10. ?
11. All three lines contain point P. Algebra
12. The three medians are concurrent. Definition of concurrent
16
What is step 10 in this proof?
Answers: 1
Mathematics, 21.06.2019 16:50, lucyamine0
The parabola y = x² - 4 opens: a.) up b.) down c.) right d.) left
Answers: 1
Mathematics, 18.05.2021 19:10
Mathematics, 18.05.2021 19:10
Mathematics, 18.05.2021 19:10