5. In the figure, angle YXZ=angleXPZ. then find ZX/ZY
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Answered by
2
Answer:
AAA postulate for symmetry :
If all three corresponding interior angles of 2 triangles are the same, then the two triangles are similar.
In general, if two corresponding angles are equal, then the remaining angle will also be equal, as they always add up to
180
o
.
In figure (i), if
∠
A
=
∠
D
,
∠
B
=
∠
E
,
∠
C
=
∠
F
by AAA postulate we can say that 2 triangles are similar.
In fig (2) given
∠
Y
X
Z
=
∠
X
P
Z
We can divide the given figure (iii) into two separate triangles.
Consider
△
X
Y
Z
and
△
P
X
Z
.
∠
Y
X
Z
=
∠
X
P
Z
....(given)
∠
X
Z
Y
=
∠
X
Z
P
...(
∵
they are same )
∠
X
Y
Z
=
∠
P
X
Z
...(
∵
sum of angles = 180°)
Hence, by AAA postulate,
△
X
Y
Z
∼
△
P
X
Z
∴
Z
X
Z
Y
=
P
Z
X
Z
....cpst
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3
b
Answer:
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