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Geometry
Examples: 4.1 – 4.4
Name:____________________________________
Date:___________________ Period:___________
4.1
In the figure, PQ  PS , PR  QS . Complete the sentence.
P
1. PQ is the ____________________ of the right triangle PQR .
2. In PQR , PQ is the side opposite angle _______________.
3. QS is the ________________ of the isosceles triangle PQS .
4. The legs of PRS are ________ and ________ .
5. ________ is the hypotenuse of PRS .
Classify the triangles by (a) its angles and (b) its sides.
6.
7.
8.
40
Q
R
S
100
9.
60
a)__________
a)__________
a)__________
a)__________
b)___________
b)___________
b)___________
b)___________
Match the triangle description with the most specific name.
10. Side lengths: 2, 3, 4
_____
A. Equilateral
11. Side lengths: 3, 2, 3
_____
B. Scalene
12. Side lengths: 4, 4, 4
_____
C. Obtuse
13. Angle measures: 60, 60, 60 _____
D. Equiangular
14. Angle measures: 30, 60, 90 _____
E. Isosceles
15. Angle measures: 20, 145, 15 _____
F. Right
Complete the statement using always, sometimes or never.
16. An isosceles triangle is ________ an equilateral triangle.
17. An obtuse triangle is ________ an isosceles triangle.
18. An interior angle of a triangle and one of its adjacent exterior angles are _______ supplementary.
19. The acute angles of a right triangle are _________ complementary.
20. A triangle ________ has a right angle and an obtuse angle.
Find the measure of the numbered angles.
21.
1
40
2
3
95
________
________
________
Find the measure of the exterior angle shown.
22.
________
2x-8
x
31
4.2
LMN  PQR . Find the following.
Q
1. m P = ________
N
2. M  _______
3. R  _______
4. m N = ________
5. PQ = ________
6. LN  ________
105
L
7. QR  ________
8. List the 6
corresponding
45
congruent parts
________________
________________
________________
________________
R
M
________________
10 cm
________________
9) Name the four methods you have learned for proving triangles congruent. Only one of these is called a
theorem. Why is it called a theorem? _____ _____ _____ _____ _____________________
P
Is it possible tp prove that the triangles are congruent? If so, state the postulate or theorem you would
use?
10) RST  TQR S
11) JKL  NML
12) DFE  JGH
K
M
F
J
L
T
R
E
N
J
D
H
G
Q
State the third congruence that must be given to prove that ABC  DEF using the indicated
postulate or theorem.
13) ASA Congruence Postulate
14) AAS Congruence Theorem
F
A
E
B D
F
B
A
C
C
D
E
LOGICAL REASONING: Is it possible to prove that the triangles are congruent? If so, state the
postulate or theorem you would use. Also state the congruent triangles.
M
B
15) R
16)
17)
S
P
S
Q
T
V
U
T
A
D
C
R
18) E
F
H
19)
X
K
M
J
20)
W
Z
G
J
N
L
Q
Y
LOGICAL REASONING: Decide whether enough information is given to prove that the triangles are
congruent. If there is enough information, tell which congruence postulate or theorem you would use.
21) ABC , DEC
22) FGH , JKH
23) PQR , SRQ
F
P
B
A
Q
G
C
H
E
D
K
S
24)
UVT , WVT
25)
R
J
LMN , TNM
26) YZW , YXW
L
T
T
Z
W
Y
X
W
N
M
U
V
27)
ACB , ECD
28)
RST , WVU
T
A
GJH , HLK
29)
U
J
G
D
L
B
C
E
W
R
S
H
K
M
V
DEVELOPING PROOF: State the third congruence that must be given to prove that PQR  STU
using the indicated postulate or theorem. (Hint: First sketch PQR and STU . Mark the triangles with
the given information.)
30) Given: Q  T , PQ  ST . Use the AAS Congruence Theorem.
31) Given: R  U , PR  SU . Use the ASA Congruence Postulate.
32) Given: R  U , P  S . Use the ASA Congruence Postulate.
Use the diagram. Name the included angle between each pair of sides given.
K
P
34) JK and KL _____
35) LP and LK _____
36) KL and JL _____
37) PK and LK _____
38) JL and JK _____
39) KP and PL _____
40) Use the same diagram to list the 6 corresponding congruent parts.
_____ _____
_____ _____
_____ _____
_____ _____
_____ _____
L
J
33) Given: PR  SU , R  U . Use the SAS Congruence Postulate.
_____ _____