worksheet congruent and similar triangle...
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© Cengage Learning Australia Pty Ltd 2013 MAT09MGWK10153 Measurement and Geometry: Geometric reasoning www.nelsonnet.com.au
worksheet
Congruent and similar triangle proofs
(For advanced students only)
Tests for congruent triangles: SSS, SAS, AAS, RHS1 Which test proves that:
a ∆ABC ≡ ∆ADC?
B
A
D
C
________
b ∆QRP ≡ ∆PNQ?
M
R N
QQN 5 PR
P
________
c ∆WZX ≡ ∆YZX?
Z
W
X
Y
________
d ∆PQO ≡ ∆SRO?QP
S R
O
________
2 AC and DB are diameters of a circle with centre O. Prove that ∆ABO ≡ ∆DCO.
D
A
C
BO
3 Prove ∆PSR ≡ ∆PQR and hence find the values of x and y.S Q
R
P
9 cm
2 cm 2 cm
xy8
958
508 508
4 a Prove that ∆KNM ≡ ∆KLM.
K M
N
L
b If NL 5 4 cm and KL 5 3 3 NM, then write the lengths of ML and KN.
__________________________________________
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© Cengage Learning Australia Pty Ltd 2013 MAT09MGWK10153 Measurement and Geometry: Geometric reasoning www.nelsonnet.com.au
5 a Prove that ∆DEH ≡ ∆FGH.D
E
H
F
G
b Name the side that has the same length as EH. _____
6 a Prove ∆OZY ≡ ∆OXY.
X
O
Y
Z
b List the three pairs of equal corresponding angles. ______________________________________
c What is special about ∠OYZ?
_________________________________________________________________________________
Tests for similar triangles: SSS, SAS, AA, RHS 7 Which test proves that:
a ∆RST ||| ∆WUV?
R S
T
3
5
1108
WV
U
9
15
1108
____________
b ∆MNP ||| ∆SQR?
M
P N
86
Q
S R
12
9
____________
c ∆HIJ ||| ∆LKM?H
I
J
1824
12
K
M
L6
4 8
____________
d ∆DEH ||| ∆FGH?
DE
FG
H
____________
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© Cengage Learning Australia Pty Ltd 2013 MAT09MGWK10153 Measurement and Geometry: Geometric reasoning www.nelsonnet.com.au
8 Prove that the triangles in each pair below are similar, then find x.
a
C
B
A
2.5
6.5
6
D
EF x
1026
x 5 ______
b M
NP
208258
4
x Q R
S
258
1358
20
x 5 ______c
GH
F
608
3
6
S
RT
608x
10
x 5 ______
d
Y
XW
V
U6
921
38.531.5
x
x 5 ______
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© Cengage Learning Australia Pty Ltd 2013 MAT09MGWK10153 Measurement and Geometry: Geometric reasoning www.nelsonnet.com.au
Answers1 a SSS b RHS c AAS d SAS2 SAS3 SAS; x 5 9 cm; y° 5 35°4 a AAS b ML 5 2 cm; KN 5 6 cm5 a AAS b GH6 a SSS b ∠Z 5 ∠X; ∠ZOY 5 ∠XOY; ∠ZYO 5 ∠XYO c It is a right angle (90°)7 a SAS b RHS c SSS d AA8 a RHS; x 5 24 b AA; x 5 8 c AA; x 5 5 d SAS; x 5 11
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