Author: Mgr. Radomír Macháň
Date: 15. listopadu 2013

C

B

A

r

p

Výška trojúhelníku je kolmá vzdálenost strany trojúhelníku 
a k ní příslušného protějšího vrcholu trojúhelníku.

Konstrukce výšek trojúhelníku

Příklad: 
Sestrojte všechny výšky daného trojúhelníku. 

△ABC

p; p⊥BC; A∈p

P_a; P_a∈p∩BC

v_a; v_a=|AP_a|

atd.:

Konstrukce:

Co je výška trojúhelníku?

p

1

2

v_a

3

P_c

P_b

4

v_b

5

6

v_c

7

2

3

P_a

v_a

4

a

b

P_b

v_b

c

d

e

P_c

v_c

f

O

8

Náčrt a rozbor:

g

5

1

Postup:

N = (16.807483971183846, 2.991503446312609)
M = (21.17212670966234, -3.4738785541438486)
L = (13.442222046656035, -2.2297514184093252)
a_2 = Line(L, M)
mnohoúhelník2, n_1, l_1, m_1 = Polygon(L, M, N)
j_1 = OrthogonalLine(N, n_1)
b_2 = Line(N, L)
q = OrthogonalLine(M, m_1)
t = Line(N, M)
m = OrthogonalLine(L, l_1)
A_1 = (0.84, 5.5)
B_1 = (9.2, 5.5)
b = Segment(A_1, B_1)
k = false
A = (2.326657634076601, 0.7933878737565576)
B = (6.895257634076601, 0.7933878737565576)
C = (5.365593427789291, 3.786928992110091)
mnohoúhelník1, e, c, d = Polygon(A, B, C)
f = OrthogonalLine(A, c)
D = Point(f)
E = Point(f)
g = Segment(D, E)
P_a = Intersect(c, g)
α = Angle(C, P_a, D)
h = false
j = false
l = Segment(A, P_a)
p = false
a_1 = OrthogonalLine(C, e)
F = Point(a_1)
G = Point(a_1)
b_1 = Segment(F, G)
H = Intersect(e, b_1)
β = Angle(B, H, C)
c_1 = OrthogonalLine(B, d)
I = Point(c_1)
J = Point(c_1)
d_1 = Segment(I, J)
K = Intersect(d, d_1)
γ = Angle(A, K, B)
v = false
e_1 = Segment(B, K)
w = false
a = false
f_1 = Segment(C, H)
z = false
n = false
o = false
O_1 = Intersect(m, t)
q_1 = Segment(L, O_1)
r = false
s = false
u = false
P = Intersect(q, b_2)
h_1 = Segment(P, M)
i_1 = false
k_1 = false
o_1 = false
Q = Intersect(j_1, a_2)
p_1 = Segment(N, Q)
r_1 = false
O = Intersect(m, q)
R = Intersect(g, l)
S = Intersect(g, l)
T = Intersect(b_1, f_1)
U = Intersect(d_1, e_1)
V = Intersect(g, l)
W = Intersect(b_1, f_1)
Z = Intersect(d_1, e_1)
C_1 = Intersect(g, l)
D_1 = Intersect(g, l)
E_1 = Intersect(g, l)
F_1 = Intersect(b_1, f_1)
G_1 = Intersect(d_1, e_1)
H_1 = Intersect(g, l)
I_1 = Intersect(e_1, f_1)
s_1 = false
t_1 = false
g_1 = false
u_1 = false
w_1 = false
i = false