NAME ______________________________________________ DATE

____________ PERIOD _____

7-1

Practice

(Average)

Geometric Mean
Find the geometric mean between each pair of numbers to the nearest tenth. 1. 8 and 12 2. 3 7 and 6 7 3. 4 and 2 5

96

9.8

126

11.2

8 5

1.3

Find the measure of each altitude. State exact answers and answers to the nearest tenth. 4. T U

5. J
V

6

M
17

5 A

12

L

K

Answers

60

7.7

102

10.1

Find x, y, and z. 6.
y
8

7.
23

25

6

x z

z

x

(Lesson 7-1)

y

184 713
8.
y
2 3

13.6; 26.7

248

15.7;

114 475
9.
z

10.7; 21.8

150

12.2;

10

z

x

x

20

y

4.5;

13

3.6; 6.5

15; 5;

300

17.3

10. CIVIL ENGINEERING An airport, a factory, and a shopping center are at the vertices of a right triangle formed by three highways. The airport and factory are 6.0 miles apart. Their distances from the shopping center are 3.6 miles and 4.8 miles, respectively. A service road will be constructed from the shopping center to the highway that connects the airport and factory. What is the shortest possible length for the service road? Round to the nearest hundredth. 2.88 mi

NAME ______________________________________________ DATE

____________ PERIOD _____

7-2
Find x. 1.
x

Practice

(Average)

The Pythagorean Theorem and Its Converse
2.
23 13 34 21

3.
26

26

x
18

x

698
4.
34

26.4
5.
22

715
x
14

26.7
6.

595
24

24.4
x
42 24

x

16

1640

40.5

60

7.7

135

11.6

Answers

Determine whether

GHI is a right triangle for the given vertices. Explain. 1) 8. G( 6, 2), H(1, 12), I( 2, 1)

7. G(2, 7), H(3, 6), I( 4,

yes; GH

2, HI

98,

no; GH

149, HI 17,
2

130,

IG

(

2)

100,

2

(

98 )

2

(

100 )
4)

IG

2

(

130 )

(

17 )

2

(
9)

149 )

2

(Lesson 7-2)

9. G( 2, 1), H(3,

1), I( 4,

10. G( 2, 4), H(4, 1), I( 1,

yes; GH

29, HI

58,

yes; GH

45, HI

125,

IG

(

29 )

29,

2

(

29 )

2

(

58 )

IG

2

(

45 )

170,

2

(

125 )

2

(

170 )

2

Determine whether each set of measures can be the measures of the sides of a right triangle. Then state whether they form a Pythagorean triple. 11. 9, 40, 41 12. 7, 28, 29 13. 24, 32, 40

...New Theorems: Parts of Similar Triangles Unit 6 Day 3
1) If two triangles are similar, then the perimeters are proportional to the measures of the corresponding sides. The ratio of the perimeters = scale factor.
2) If two triangles are similar, the measures of the corresponding altitudes are proportional to the measure if the corresponding sides.
3) If the two triangles are similar. The the measures of the corresponding...

...figure given below, AC is parallel to BD. Is
A E D B C
OR Prove that:
sin A + cos A sin A − cos A 2 + = sin A − cos A sin A + cos A sin 2 A − cos 2 A
AE DE = ? Justify your answer. CE BE
21. Observe the graph given below and state whether triangle ABC is scalene, isosceles or equilateral. Justify your answer. Also find its area.
15. A bag contains 5 red, 8 green and 7 white balls. One ball is drawn at random from the bag, find the probability of getting (i) a white...

...PLAN WEEK 5
Dr. Tonjes September 2011
LESSON: Oblique Triangles, Laws of Sines and Cosines
INTRODUCTION:
Student will demonstrate how to apply laws of sines and cosines to oblique triangles.
OBJECTIVES:
After completing this unit, the student will be able to:
6. Use the Law of Sines and the Law of Cosines to solve oblique triangle problems.
6.1. Summarize the Law of Sines.
6.2. Find the area of an oblique triangle...

...PERIOD
FEATURES
REMARKABLE CHANGES
PRE-SPANISH PERIOD
Do not have an organized system of education as we have now.
They followed their code of laws “the Code of Kalantiao and Maragtas.
Ideas and facts were acquired through suggestion, observation, example and imitation.
The youngsters learned by experienced and the learned more in occupational.
The inhabitants were civilized people, possessing their system of writing, laws and moral standards in...

...upon a body, in equilibrium, may be represented by a triangle of forces. (Vector addition)
INTRODUCTION
With this experiment we will show that a body in a state of equilibrium, with three forces acting in a singular plane. The following conditions must be met:
* Moment of all three forces must pass through the same point.
* Magnitudes of the forces can be represented by the sides of a triangle, each as a vector with the side of the triangle...

...
5C Problems involving triangles
cQ1. The diagram shows a sector AOB of a circle of radius 15 cm
and centre O.
The angle at the centre of the circle is 115.
Calculate (a) the area of the sector AOB.
(b) the area of the shaded region. (226 , 124
nQ2. Consider a triangle and two arcs of circles.
The triangle ABC is a right-angled isosceles
triangle, with AB = AC = 2.
The point P is...

...given non - collinear points is:
[Marks:1]
A.
Two
B.
infinitely many
C.
Four
D.
Three
6]
The area of a right triangle with base 5 m and altitude 12 m is
[Marks:1]
A.
50 m2
B.
15 m2
C.
9 m2
D.
30 m2
7]
Evaluate: 53 - 23 - 33
[Marks:1]
A.
80
B.
60
C.
120
D.
90
8]
The area of an equilateral triangle of side 14 cm is
[Marks:1]
A.
B.
C.
D.
9]
Simplify:
[Marks:2]...

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