Download (2) The student is correct in part a and part b, but not

(2) The student is correct in part a and part b, but not in part c. (c) is not
distorted because the ratio of the sides 88 is the same as the ratio of the
picture 66 . I would give the student 7 points for the two correct answers.
(3) (a) The sum of the measures of the angles of a triangle is 180 degrees, so
90 + 20 + C = 180. Hence 110 + C = 180. So C = 70 degrees
(b) Since the two triangles are similar, D is congruent to A, so D has measure
20 degrees.
(c) Since the two triangles are similar, F is congruent to C, so F has measure
70 degrees.
(7) Since the triangles are similar, the sides are proportional. So
cross multiplying we find tha 150 = 25x. Hence x = 6. Also
cross multiplying we find tha 200 = 25y. Hence y = 8.
30
x
40
y
=
=
25
5 .
25
5 .
By
By
(9) (a) Since the sum of the measures of the angles of a triangle is 180 degrees,
25 + 120 + F = 180. So 145 + F = 180. Hence F = 35. Since the triangles
have two pairs of congruent angles, they are similar by the A-A similarity
postulate.
(b) The triangles are not similar because triangle DEF has a 42 degree angle
and triangle ABC has a 43 degree angle, and the two sides between the
angles are proportional. There’s no way that the 2 triangles can have
congruent angles while still keeping the proportional sides proportional.
25
21.65
(c) 12.5
5 = 10 = 8.66 = 2.5. Hence the sides are proportional, and so the
triangles are similar by the S-S-S similarity theorem.
(11) The polygons have corresponding angles that are congruent, so we just need
45
125
65
= 60
to check and see if the sides are proportional. 13
12 = 9 = 25 = 5. Hence
the polygons are similar.
(17) The two triangles have 2 pairs of congruent angles. B is congruent to C and
E is congruent to D. So by the A-A similarity postulate, the two triangles
are similar
(19) The sides of the triangle are not proportional since
the triangle is not similar.
18
12
= 23 , but
12
9
= 43 . Hence
(21) In real life we say that two objects are similar if they look the same, but in
mathematics two objects are similar if they have the same shape, but not
necessarily the same size. For example, a triangle with angles measuring 90,
30, and 60 degrees and a triangle whose angles measure 90, 31 , and 59 degrees
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are not similar in the sense of mathematics, but they are similar in real life
since they look almost alike.
(23) For two triangles to be similar they need to have 2 pairs of congruent angles,
not just one pair. So just because 2 triangles are right triangles, it doesn’t
mean that they have to be similar triangles. I would encourage the student
to review the postulates and theorems for similarity.
(27) (a) The two triangles are similar by the A-A postulate. They both have
right angles, and the shared angle of the two triangles is the second pair
of congruent angles.
(b) Since corresponding sides of similar triangles are proportional, we know
x
that 38
8 = 6 . Hence 8x = 228 and x = 28.5. So the house is 28.5 ft tall.