10^{th} Triangle (Similarity)
Practice Questions For SA-1 By JSUNIL |

Similar figures: “Two
similar figures have the same shape but not necessarily the same sizes are
called similar figures. “ This verifies that congruent figures are similar but
the similar figures need not be congruent.

__Conditions for similarity of polygon__: Two polygons of the same number of sides are similar, if

(i) Their corresponding
angles are equal and

(ii) Their corresponding
sides are in the same ratio (or proportion).

Note: The same ratio of the
corresponding sides is referred to as the
scale factor (or the Representative
Fraction) for the polygons.

Equiangular triangles: If corresponding angles of two triangles are
equal, then they are known as equiangular triangles.

A famous Greek mathematician
Thales gave

__an important truth relating to two equiangular triangles__which is as follows: “The ratio of any two corresponding sides in two equiangular triangles is always the same.”
Q.

__The Basic Proportionality Theorem__(now known as the Thales Theorem) : “If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. “ [Prove it.]
Q.

__The converse of The Basic Proportionality Theorem:__If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side. [Prove it by contradiction methods]
Q.
In a triangle ABC, E and F are point on AB and AC and EF || BC. Prove that AB/AE = AC/AF

Q.
Prove that a line drawn through the mid-point of one side of a triangle
parallel to another side bisects the third side.

Q.
Prove that the line joining the mid-points of any

two
sides of a triangle is parallel to the third side.

Q.
In a triangle ABC, E and F are point on AB and AC Such that AE/EB = AF/FC and
<AEF =<ACB. Prove that ABC is an isosceles Triangle.

Q.
In a trapezium ABCD , AB || DC and E and
F are points on non-parallel sides AD and BC respectively such that EF is
parallel to AB .Show that AE/ ED = BF /FC [join AC to intersect EF at G]

Q.
In a trapezium ABCD , AB || DC and its
diagonals intersect each other at the point O. Show that AO/ BO = CO/DO

Q.
If the diagonals of a quadrilateral divide each other proportionally, then it
is a trapezium.

Q. In
ΔABC, DE || BC

(a)
IF AD /DB = 2/3 and AC = 18cm, find AE.

(b)
IF AD = x, DB = x – 2 , AE = x + 2, EC = x -1, find x.

(c)
If AD = 8cm, AB = 12cm, AE = 12cm, find CE.

Q. In
the given figure, AB || DC. If EA = 3x - 19, EB = x - 4, EC = x - 3 and ED = 4,
find x.

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