Author: BENNY VARGHESE
Date: 19/10/2006

vvvvv

Class 10: THALES THEOREM

A presentation by:
Benny Varghese 
PGT Maths 
JNV Pathanamthitta

Click the checkboxes “line II BC” ,“line II AC” or
 “line II AB” as you please. Drag D, I, L to change
 the position of parallel line and observe the ratios
of segments given on RHS
drag A,B,C to change triangle

Line ∥BC

⇒\frac{AE}{EB}=\frac{AF }{FC }

⇒\frac{BH}{HC}=\frac{BG}{GA}

Line ∥AC

⇒\frac{CM}{MA}=\frac{ CN }{ NB } 

Line∥AB

AIM

To understand the concept of THALES THM

How to proceed with?

A = (4.185364583333333, 5.159947916666663)
B = (-0.5534895833333329, -0.25083333333333646)
C = (11.824114583333332, -2.478802083333336)
P, c, a_2, b_1 = Polygon(A, B, C)
D = (4.609739583333332, 2.719791666666665)
d = Line(D, a_2)
F = Intersect(b_1, d)
E = Intersect(c, d)
δ: Distance[A, E] / Distance[E, B]
ε: Distance[A, F] / Distance[F, C]
AE = Distance(A, E)
EB = Distance(E, B)
i = Distance(A, F)
j = Distance(F, C)
distanceAE = Distance(A, E)
perimeterP = Perimeter(P)
G_1 = Point(d)
H_1 = Point(d)
e = false
f: AE / EB
text1: "\frac{AE}{EB}=\frac{" + (LaTeX[AE]) + "}{" + (LaTeX[EB]) + "}=" + (LaTeX[f]) + "
 "
AF = Distance(A, F)
FC = Distance(F, C)
g: AF / FC
text2: "\frac{AF}{FC}=\frac{ " + (LaTeX[AF]) + "}{" + (LaTeX[FC]) + " }= " + (LaTeX[g]) + ""
I = (2.5232291666666664, 0.5625520833333321)
h = Line(I, b_1)
J = Point(h)
K = Point(h)
G = Intersect(h, c)
H = Intersect(a_2, h)
w = Vector(I, J)
k = Vector(I, K)
l = Line(D, a_2)
N_1 = Point(l)
O = Point(l)
u = Vector(D, N_1)
v = Vector(D, O)
BH = Distance(B, H)
HC = Distance(H, C)
BG = Distance(B, G)
GA = Distance(G, A)
m: BH / HC
text5: "\frac{BH}{HC}=\frac{" + (LaTeX[BH]) + "}{" + (LaTeX[HC]) + "}=" + (LaTeX[m]) + ""
n: BG / GA
text6: "\frac{BG}{GA}=\frac{" + (LaTeX[BG]) + " }{" + (LaTeX[GA]) + " }= " + (LaTeX[n]) + ""
o = false
L = (7.827916666666665, -0.3922916666666677)
p = Line(L, c)
M = Intersect(b_1, p)
N = Intersect(a_2, p)
R = Point(p)
S = Point(p)
q = Vector(L, R)
r = Vector(L, S)
CM = Distance(C, M)
MA = Distance(M, A)
CN = Distance(C, N)
NB = Distance(N, B)
MB = Distance(M, B)
t: CM / MA
text8: "\frac{CM}{MA}=\frac{ " + (LaTeX[CM]) + " }{ " + (LaTeX[MA]) + " }=  " + (LaTeX[t]) + ""
s: CN / NB
text12: "\frac{CN}{NB}=\frac{ " + (LaTeX[CN]) + " }{ " + (LaTeX[NB]) + " }= " + (LaTeX[s]) + " "
a_1 = false
a: false
b = false