Download CHAPTER 5 (5.3, 5.5, 5.6)

TRIANGLE
INEQUALITIES
CHAPTER 5
(5.3, 5.5, 5.6)
5.3– Inequalities of One Triangle 1. Measure and label the sides and angle measures of each triangle below: L 2. Put the angles in order from least to greatest using inequalities. 3. Put the sides in order from shortest to longest using inequalities. A K
C
B Angles: ____________________
Sides: _____________________
M
Angles: ____________________
Sides: _____________________ T W
Y
R V
Angles: ____________________ Sides: _____________________ Angles: ____________________ Sides: _____________________ How are inequalities related to sides and angles of triangles? X
EX: List the sides in order from longest to shortest. EX: List the angles in order from smallest to largest. Exterior Angle Inequality Theorem 3 1 2
4
Kuta Software - Infinite Geometry
Name___________________________________
Inequalities in One Triangle
Date________________ Period____
Order the angles in each triangle from smallest to largest.
1)
2)
16 yd
L
K
J
18 cm
14 yd
18 yd
L
13 cm
M
20 cm
K
3) In ∆RQP
QP = 15 ft
RP = 25 ft
RQ = 13 ft
4) In ∆TUV
UV = 17 yd
TV = 14 yd
TU = 9 yd
Name the largest and smallest angle in each triangle.
5)
6)
D
20 ft
16 ft
C
Y
17 ft
19 ft
B
7) In ∆UVW
VW = 13 m
UW = 11.7 m
UV = 5.8 m
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X
17 ft
20 ft
W
8) In ∆EFG
FG = 10.9 in
EG = 17 in
EF = 10.9 in
-1-
Worksheet by Kuta Software LLC
Order the sides of each triangle from shortest to longest.
9)
10)
F
L
98°
46°
M
55°
36°
63°
62°
N
E
G
11) In ∆VWX
m∠V = 50°
m∠W = 48°
m∠X = 82°
12) In ∆STU
m∠S = 50°
m∠T = 70°
m∠U = 60°
Name the longest and shortest side in each triangle.
13)
A
14)
F
66°
46°102°
C
48°
B
15) In ∆DEF
m∠D = 35°
m∠F = 95°
E
66°
D
16) In ∆KLM
m∠K = 50°
m∠L = 100°
m∠M = 30°
Critical thinking questions:
17) In triangle ABC:
AB is the longest side.
70° is the measure of angle B.
18) In triangle XYZ:
XY is the shortest side.
30° is the measure of angle Y.
Find the range of possible measures for
angle A.
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Find the range of possible measures for
angle X.
-2-
Worksheet by Kuta Software LLC
5.5– Triangle Inequality Theorem 1. Draw a triangle with side lengths of 3cm, 4cm, 5cm. 2. Draw a triangle with side lengths of 3cm, 5cm, 7cm. 3. Draw a triangle with side lengths of 3cm, 3cm, 6cm. 4. Draw a triangle with side lengths of 4cm, 5cm, 11cm. Triangle Inequality Theorem Examples: Could the following side lengths make a triangle? Why or why not? 1) 5, 7, 9 2) 3, 2, 11 3) 6, 7, 13 4) 21, 18, 12 5) 7, 14, 7 6) 5, 21, 24 Examples: What are the possible values for the third side of the triangle? 1) x, 7, 4 2) 13, x, 8 3) 4, 4, x 4) 6, 11, x‐2 5) x+1, 14, 9 5.6– Inequalities in Two Triangles Find the measurements of the lengths of the segments and the measures of the angles between them. Hinge Theorem Converse of the Hinge Theorem EX: Which angle (∠1 or ∠2) is smaller? EX: Given that ST  PR , PT = 12 and SR = 10, how does ∠PST compare to ∠SPR? EX: Find the value of x. EX: Name the longest segment in figure ABCD. Section 5-6 Worksheet
Inequalities in Two Triangles
I. Complete with <, >, or =.
1.
AB _______ DE
4.
m1 _______ m2
m1 _______ m2
2. FG _______ LM
3.
5.
6. m1 _______ m2
MS _______ LS
II. Match the conclusion on the right with the given information. Use the diagram below.
_______ 7. AB  BC , 1  m2
A. m7  m8
_______ 8. AE  EC , AD  CD
B. AD  AB
_______ 9. m9  m10, BE  ED
C. m3  m4  m5  m6
_______ 10. AB  BC , AD  CD
D. AE  EC
III. Use the inequality to describe the restriction on the value of x as determined by the Hinge Theorem
or its converse.
11.
12.
13.