Download 5.5 Triangle Inequalities

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Date
Per.
REVIEW Chapter 5B: Triangle Inequalities and Right Triangles
5.5 Triangle Inequalities
2, Write the sides of AGHI in order from
shortest to longest.
1. Write the angles in order from smallest to
largest.
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3. List the sides of A A B C in order from shortest to longest.
B
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4. Short Answer, Explain how you use the Triangle inequality Theorem to determine if 3 segments
make a triangle. T^K-d^ secjynej^ rrucJc^
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5. Tell whether a triangle can have the given sides with lengths. Show all three inequalities to find
b . ]\A ^'5-- Q >5~- ^ ^
your answer,
a. 6, 10, and 15 ^
1o - f l S > ^
b. 11.9, 5.8,and 5.8 /\ D
6. Aaron, Brandon, and Clara sit in class so that they form the vertices of a triangle. Aaron is 15 feet
from Brandon and it is 8 feet from Brandon to Clara. Give the range of possible distances from
Aaron to Clara.
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, / \? ^ ^ •'S'-^S
B
5
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7. Multiple Choice. If the lengths of two sides of a triangle are 4 and 10, what could be the length of
the third side?
A. 6
C. 14 •
D.16
Answers on website
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^14
8. Multiple Choice. On the banks of a river, surveyors marked locations A, B, and C. The measure of
ZACB = 70° and the measure of ZABC = 65°.
B
- 135
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Which expression shows the relationship between the lengths of the sides of this triangle?
A.
AB<BC<AC
B.
BC<AB<AC
^BC<AC<AB
D.
AC<AB<BC
9. Multiple Choice. As shown in the diagram of LACD below, B is a point on
and DB is drawn.
-Jiz.
If mZA = 66, mZCDB = 18, and mZC= 24, what is the longest side of LABDl
AB
G.
n.AD
J.
10. List the angles of A J K L in order from smallest to largest. J (-10, -4), K (0, 3), L (2, -8). Use the
distance formula to find the length of each side.
5.7 Pythagorean Theorems and Inequalities
11. Use the Pythagorean Theorem to find the value of x. Express your answer in simplest radical
form.
Answers on website
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12. In the diagram below of /\ADB, mZBDA =90, AD= 5^2, and AB = 2 V l 5 .
What is the length of BD ?
13. Short Answer. List the two conditions that have to be true for 3 numbers to be a Pythagorean
Triple. Give an example with your explanation.
14. For each triangle: I. Find the missing side length. 2. Tell if the side lengths form a Pythagorean triple.
B.
15. Use the picture on the right to find the missing sides
a. Find x
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T
b. F i n d y _ J l _
12""+(^""r/15
16. Short Answer. Explain how you use the Pythagorean Theorem and Pythagorean InequaHties to
classify a triangle as acute, obtuse, or right.
a.^J^-^/ ycf^ O-cuAC
17. Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse,
or right
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a. 7, 12, 16
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b. 8, 13, 23
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18. The aspect ratio of a T V screen is the ratio of the width to the height of the image. A regular T V
has an aspect rado of 4:3. Find the height and width of a 42-inch T V screen to the nearest tenth
of an inch. (The measure given is the length of the diagonal across the screen.) See p. 349 Example 2
19. The length of a leg of right triangle is two times the length of the other leg. The hypotenuse has
length 25. What is the length of the longer leg?
Answers on website
5
20. In the figure below, what is the length of ML in centimeters?
28 cm
n
M
N
5.8 Special Right Triangles
21. In the figure, what is the value of x?
A.
B.
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X
X y
22. What is the value of z?
I
23. Triangle A B C is an equilateral triangle with side lengths of 10
inches. What is the length ofADl
\\o
D
24.
iov5
Answers on website
3
26. A billboard is supported by 20-foot long tubes at an angle of 60°. How far from the bottom of the
billboard is bottom end of the brace?
30 1
y
2,D
10
227. A kite string is 220 feet long from the kite to the ground. The string makes a 45° angle with the ground.
About how high off the ground is the kite?
G 127 ft
^'^^^
J 311ft
28. Multiple Choice. The field inside a major league baseball diamond is a square, 90 feet on a side,
as show in the diagram below. To the nearest tenth of a foot, what is the distance from first base
to a point on the line between second base and third base, exactly halfway between the two bases?
A.
C.
D.
63.6 feet
100.6 feet
127.3 feet
135.0 feet
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29. Short Answer. The length of the shorter leg of a 30-60-90 triangle is 20cm. Find the length of
the altitude to the hypotenuse. Explain how you arrived at your answer. ,
30. What is the inverse of the statement below?
If a triangle is scalene, then no two angles are congruent.
If the triangle is not scalene, then there are two congruent angles.
B. If two angles of a triangle are congruent, then the triangle is scalene.
C. If there are two congruent angles in a triangle, then the triangle is not scalene.
D. If the triangle is not scalene, then there are no congruent angles.
Answers on website
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