Regents Exam Questions G.G.44: Similarity Proofs
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G.G.44: Similarity Proofs: Establish similarity of triangles, using the following
theorems: AA, SAS, and SSS
1 In the diagram below of
.
, Q is a point on
, S is a point on
Which reason justifies the conclusion that
1) AA
2) ASA
3) SAS
4) SSS
2 In the diagram of
and
below,
Which method can be used to show that
1) SAS
2) AA
3) SSS
4) HL
,
is drawn, and
?
and
intersect at C, and
must be similar to
?
.
Regents Exam Questions G.G.44: Similarity Proofs
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3 In the diagram below,
and
intersect at T,
is drawn, and
What technique can be used to prove that
1) SAS
2) SSS
3) ASA
4) AA
4 In triangles ABC and DEF,
could be used to prove
1) AA
2) SAS
3) SSS
4) ASA
,
?
,
?
.
,
, and
. Which method
Regents Exam Questions G.G.44: Similarity Proofs
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5 For which diagram is the statement
1)
not always true??
2)
3)
4)
6 In
and
,
?
1)
2)
3)
4)
. Which additional information would prove
Regents Exam Questions G.G.44: Similarity Proofs
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7 In the accompanying diagram of circle O, diameter
the circle at B, E is a point on the circle, and
Prove:
8 The diagram below shows
is similar to
.
9 In the diagram below,
.
, with
,
,
,
is drawn, tangent
.
, and
, and
is drawn to
. Prove that
. Prove that
Regents Exam Questions G.G.44: Similarity Proofs
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10 Given: chords
and
and
are drawn.
of circle O intersect at E, an interior point of circle O; chords
Prove:
11 In the accompanying diagram,
.
and
and
intersect at point T. Prove that
Regents Exam Questions G.G.44: Similarity Proofs
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1
2
3
4
5
6
7
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
1
2
4
2
4
3
REF:
REF:
REF:
REF:
REF:
REF:
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, the angle formed by tangent
and diameter
is a right angle. The measure of an inscribed
angle is half that of its intercepted arc. Because
intercepts a semicircle,
is also a right angle.
Since
,
and
are alternate interior angles and congruent. Therefore
by AA
REF: 080627b
8 ANS:
is given.
AA.
because of the reflexive property. Therefore
because of
REF: 081133ge
9 ANS:
and
are right angles because of the definition of perpendicular lines.
because all right
angles are congruent.
and
are supplementary and
and
are supplementary
because of the definition of supplementary angles.
because angles supplementary to
congruent angles are congruent.
because of AA.
REF: 011136ge
10 ANS:
and
are congruent vertical angles. Because
and
intercept the same arc, they are
congruent.
by AA. Because corresponding sides of similar triangles are in proportion,
. Cross-multiplying,
.
REF: 060133b
11 ANS:
and
are congruent vertical angles. Since
,
and
are alternate interior
angles and congruent and
and
are alternate interior angles and congruent. Therefore
by AA. Because corresponding sides of similar triangles are in proportion,
Cross-multiplying,
REF: 010833b
.
.