given: δabc
prove: the medians of δabc are concurrent.
proof:
statements...
Mathematics, 01.10.2019 18:00 kam3864
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
19
what is step 10 in this proof?
a.
statement: point p lies on line c'd'.
reason: the coordinates of p satisfy the equation of line c'd'.
b.
statement: all three lines share point p.
reason: definition of midpoint
c.
statement: line a'e' and line a'e' are concurrent.
reason: definition of concurrence
d.
statement: two of the three medians share point p.
reason: using point-slope formula
e.
statement: point p lies on line a'e' and line a'e'.
reason: algebra
Answers: 3
Mathematics, 21.06.2019 17:50
Which of these triangle pairs can be mapped to each other using two reflections?
Answers: 1
Mathematics, 21.06.2019 21:00
Sue's average score for three bowling games was 162. in the second game, sue scored 10 less than in the first game. in the third game, she scored 13 less than in the second game. what was her score in the first game?
Answers: 2
Mathematics, 22.06.2019 00:30
1.3.25 question suppose 40​% of all voters voted for a particular candidate. to simulate exit polls regarding whether or not voters voted for this​ candidate, five random samples of size 1010 and five random samples of size 10001000 have been generated using technology using a population proportion of 0.400.40​, with the accompanying results. complete parts a through c below. click the icon to view the simulation results. a. observe how the sample proportions of successes vary around 0.400.40. simulation compared to sample prop simulation compared to sample prop 1 ▾ 6 ▾ greater than 0.40 less than 0.40 equal to 0.40 2 ▾ less than 0.40 greater than 0.40 equal to 0.40 7 ▾ greater than 0.40 less than 0.40 equal to 0.40 3 ▾ greater than 0.40 less than 0.40 equal to 0.40 8 ▾ equal to 0.40 greater than 0.40 less than 0.40 4 ▾ greater than 0.40 equal to 0.40 less than 0.40 9 ▾ less than 0.40 greater than 0.40 equal to 0.40 5 ▾ equal to 0.40 less than 0.40 greater than 0.40 10 ▾ equal to 0.40 greater than 0.40 less than 0.40 click to select your answer(s) and then click check answer. 2 parts remaining clear all check answer
Answers: 3
Spanish, 05.05.2020 03:09
History, 05.05.2020 03:09
Mathematics, 05.05.2020 03:09
Mathematics, 05.05.2020 03:09
Mathematics, 05.05.2020 03:09
Mathematics, 05.05.2020 03:09
Mathematics, 05.05.2020 03:09
Advanced Placement (AP), 05.05.2020 03:09
Physics, 05.05.2020 03:09
Physics, 05.05.2020 03:09
Mathematics, 05.05.2020 03:10
Mathematics, 05.05.2020 03:10
Mathematics, 05.05.2020 03:10