Regents Exam Questions G.SRT.B.5: Similarity 4 Name: ________________________
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1
G.SRT.B.5: Similarity 4
1 In the diagram shown below, altitude
CD
is drawn
to the hypotenuse of right triangle ABC.
Which equation can always be used to find the
length of
AC
?
1)
AC
CD
=
CD
AD
2)
CD
AC
=
AC
AB
3)
AC
CD
=
CD
BC
4)
AB
AC
=
AC
AD
2 In the diagram of
CAT
below,
m∠A = 90°
and
altitude
AE
is drawn from vertex A.
Which statement is always true?
1)
CE
AE
=
AE
ET
2)
AE
CE
=
AE
ET
3)
AC
CE
=
AT
ET
4)
CE
AC
=
AC
ET
3 In the diagram below of right triangle ABC, altitude
CD
intersects hypotenuse
AB
at D.
Which equation is always true?
1)
AD
AC
=
CD
BC
2)
AD
CD
=
BD
CD
3)
AC
CD
=
BC
CD
4)
AD
AC
=
AC
BD
Regents Exam Questions G.SRT.B.5: Similarity 4 Name: ________________________
www.jmap.org
2
4 In the accompanying diagram of right triangle ABC,
altitude
BD
is drawn to hypotenuse
AC
.
Which statement must always be true?
1)
AD
AB
=
BC
AC
2)
AD
AB
=
AB
AC
3)
BD
BC
=
AB
AD
4)
AB
BC
=
BD
AC
5 In the diagram below of right triangle KMI, altitude
IG
is drawn to hypotenuse
KM
.
If
KG = 9
and
IG = 12
, the length of
IM
is
1) 15
2) 16
3) 20
4) 25
6 In the diagram below of right triangle ABC, altitude
BD
is drawn to hypotenuse
AC
.
If
BD = 4
,
AD = x − 6
, and
CD = x
, what is the
length of
CD
?
1) 5
2) 2
3) 8
4) 11
7 In the diagram below of right triangle MET,
altitude
ES
is drawn to hypotenuse
MT
.
If
ME = 6
and
SM = 4
, what is MT?
1) 9
2) 8
3) 5
4) 4
Regents Exam Questions G.SRT.B.5: Similarity 4 Name: ________________________
www.jmap.org
3
8 In the diagram below of right triangle EFG, altitude
FH
intersects hypotenuse
EG
at H.
If
FH = 9
and
EF = 15
, what is EG?
1) 6.75
2) 12
3) 18.75
4) 25
9 In right triangle RST below, altitude
SV
is drawn to
hypotenuse
RT
.
If
RV = 4.1
and
TV = 10.2
, what is the length of
ST
, to the nearest tenth?
1) 6.5
2) 7.7
3) 11.0
4) 12.1
10 In the diagram below of
ABC
,
∠
ABC
is a right
angle,
AC = 12
,
AD = 8
, and altitude
BD
is drawn.
What is the length of
BC
?
1)
42
2)
43
3)
45
4)
46
11 In the diagram below of right triangle MDL,
altitude
DG
is drawn to hypotenuse
ML
.
If
MG = 3
and
GL = 24
, what is the length of
DG
?
1) 8
2) 9
3)
63
4)
72
Regents Exam Questions G.SRT.B.5: Similarity 4 Name: ________________________
www.jmap.org
4
12 In right triangle ABC, altitude
CD
is drawn to
hypotenuse
AB
. If
AD = 4
and
CD = 8
, the length
of
BD
is
1)
48
2)
80
3) 12
4) 16
13 Line segment CD is the altitude drawn to
hypotenuse
EF
in right triangle ECF. If
EC = 10
and
EF = 24
, then, to the nearest tenth, ED is
1) 4.2
2) 5.4
3) 15.5
4) 21.8
14 In right triangle RST, altitude
TV
is drawn to
hypotenuse
RS
. If
RV = 12
and
RT = 18
, what is
the length of
SV
?
1)
65
2) 15
3)
66
4) 27
15 Kirstie is testing values that would make triangle
KLM a right triangle when
LN
is an altitude, and
KM = 16
, as shown below.
Which lengths would make triangle KLM a right
triangle?
1)
LM
=
13
and
KN
=
6
2)
LM
=
12
and
NM
=
9
3)
KL
=
11
and
KN
=
7
4)
LN
=
8
and
NM
=
10
16 In the diagram below,
CD
is the altitude drawn to
the hypotenuse
AB
of right triangle ABC.
Which lengths would not produce an altitude that
measures
62
?
1)
AD
=
2
and
DB
=
36
2)
AD
=
3
and
AB
=
24
3)
AD
=
6
and
DB
=
12
4)
AD
=
8
and
AB
=
17
Regents Exam Questions G.SRT.B.5: Similarity 4 Name: ________________________
www.jmap.org
5
17 In
RST
shown below, altitude
SU
is drawn to
RT
at U.
If
SU = h
,
UT = 12
, and
RT = 42
, which value of h
will make
RST
a right triangle with
∠RST
as a
right angle?
1)
63
2)
6 10
3)
6 14
4)
6 35
18 In the diagram of right triangle ABC,
CD
intersects
hypotenuse
AB
at D.
If
AD = 4
and
DB = 6
, which length of
AC
makes
CD ⊥ AB
?
1)
26
2)
2 10
3)
2 15
4)
42
19 In the diagram below of right triangle ACB, altitude
CD
is drawn to hypotenuse
AB
,
AD = 2
and
AC = 6
.
Determine and state the length of
AB
.
20 In the diagram below of right triangle BAL, altitude
AD
is drawn to hypotenuse
BDL
. The length of
AD
is 6.
If the length of
DL
is four times the length of
BD
,
determine and state the length of
BD
.
Regents Exam Questions G.SRT.B.5: Similarity 4 Name: ________________________
www.jmap.org
6
21 Right triangle STR is shown below, with
m∠T = 90°
. Altitude
TQ
is drawn to
SQR
, and
TQ = 8
.
If the ratio
SQ :QR
is
1:4
, determine and state the
length of
SR
.
22 In right triangle PRT,
m∠P = 90°
, altitude
PQ
is
drawn to hypotenuse
RT
,
RT = 17
, and
PR = 15
.
Determine and state, to the nearest tenth, the length
of
RQ
.
23 In right triangle ABC shown below, altitude
CD
is
drawn to hypotenuse
AB
. Explain why
ABC ∼ ACD
.
24 In the diagram below, the line of sight from the
park ranger station, P, to the lifeguard chair, L, on
the beach of a lake is perpendicular to the path
joining the campground, C, and the first aid station,
F. The campground is 0.25 mile from the lifeguard
chair. The straight paths from both the
campground and first aid station to the park ranger
station are perpendicular.
If the path from the park ranger station to the
campground is 0.55 mile, determine and state, to
the nearest hundredth of a mile, the distance
between the park ranger station and the lifeguard
chair. Gerald believes the distance from the first
aid station to the campground is at least 1.5 miles.
Is Gerald correct? Justify your answer.
ID: A
1
G.SRT.B.5: Similarity 4
Answer Section
1 ANS: 4 REF: 062422geo
2 ANS: 1 REF: 012418geo
3 ANS: 1 REF: 081916geo
4 ANS: 2
AB = 10
since
ABC
is a 6-8-10 triangle.
6
2
= 10x
3.6 = x
REF: 081820geo
5 ANS: 3
12
2
= 9 ⋅ GM
GM = 16
IM
2
= 16 ⋅ 25
IM = 20
REF: 011910geo
6 ANS: 3
x(x − 6) = 4
2
x
2
− 6x − 16 = 0
(x − 8)(x + 2) = 0
x = 8
REF: 081807geo
7 ANS: 1
6
2
= 4x
x = 9
REF: 012412geo
8 ANS: 3
12x = 9
2
12x = 81
x =
82
12
=
27
4
6.75 + 12 = 18.75
REF: 062213geo
9 ANS: 4
x
2
= 10.2 × 14.3
x ≈ 12.1
REF: 012016geo
ID: A
2
10 ANS: 2
x
2
= 12(12 − 8)
x
2
= 48
x = 43
REF: 011823geo
11 ANS: 4
x
2
= 3 × 24
x = 72
REF: 012315geo
12 ANS: 4
8
2
= 4x
64 = 4x
16 = x
REF: 062416geo
13 ANS: 1
24x = 10
2
24x = 100
x ≈ 4.2
REF: 061823geo
14 ANS: 2
18
2
= 12(x + 12)
324 = 12(x + 12)
27 = x + 12
x = 15
REF: 081920geo
15 ANS: 2
12
2
= 9 ⋅ 16
144 = 144
REF: 081718geo
16 ANS: 2
3 ⋅ 21 = 63 = 37
REF: 011622geo
ID: A
3
17 ANS: 2
h
2
= 30 ⋅ 12
h
2
= 360
h = 6 10
REF: 061613geo
18 ANS: 2
x
2
= 4 ⋅ 10
x = 40
x = 2 10
REF: 081610geo
19 ANS:
6
2
= 2(x + 2)
36 = 2x + 4
32 = 2x
16 = x
;
16 + 2 = 18
REF: 062330geo
20 ANS:
4x ⋅ x = 6
2
4x
2
= 36
x
2
= 9
x = 3
REF: 082229geo
21 ANS:
4x ⋅ x = 8
2
4x
2
= 64
x
2
= 16
x = 4
4 + 4(4) = 20
REF: 082330geo
ID: A
4
22 ANS:
17x = 15
2
17x = 225
x ≈ 13.2
REF: 061930geo
23 ANS:
If an altitude is drawn to the hypotenuse of a triangle, it divides the triangle into two right triangles similar to each
other and the original triangle.
REF: 061729geo
24 ANS:
x = .55
2
−.25
2
≅ 0.49
No,
.49
2
=.25y
.9604 = y
.9604 +.25 < 1.5
REF: 061534geo
