Similar Triangle Proof - Triangles, Math, Class 9 Video Lecture - Class 9 | Best Video for Class 9

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comm in this example we're asked to
determine if each of the following pairs
of triangles are similar in Part A
notice that we're only given one pair of
congruent angles the 60 degree angles
but remember that the sum of the
measures of the angles of a triangle is
180 degrees so we can determine that the
measure of the missing angle of the
first triangle is 55 degrees because 65
plus 60 plus 55 equals 180 now we have
two pairs of congruent angles the 55
degree angles and the 60 degree angles
therefore since two of the angles of one
triangle are congruent to two of the
angles of the other triangle we can say
that yes the triangles are similar by
the angle-angle similarity postulate
in Part B since we're given that the
lines at the top and the bottom of the
figure are parallel we can mark the
alternate interior angles at the upper
left and lower right as congruent
because if two parallel lines are cut by
a transversal then alternate interior
angles are congruent notice however that
there are no other pairs of angles that
can be marked as congruent so we do not
know if these triangles are similar
because we only have one pair of
congruent angles so we cannot use the
angle-angle similarity postulate in this
situation we write that the triangle
similarity cannot be determined
in Part C notice that the small triangle
and the large triangle both have a right
angle also notice that these triangles
share the angle at the lower left of the
figure so we can mark this angle as
congruent to itself therefore since two
of the angles of the smaller triangle
are congruent to two of the angles of
the larger triangle we can say that yes
these triangles are similar by the
angle-angle similarity postulate