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## #1 2017-05-11 02:57:04

taylorn5683
Member
Registered: 2017-02-01
Posts: 10

Exercises:
Note: we'll need some definitions about some particular kinds of angles: Right angle: 90o Acute angle: <90o Obtuse angle: >90o

1.  How many right angles can there be in a triangle?
correct

2. How many acute angles can there be in a triangle?

3. How many obtuse angles can there be in a triangle?

4. What is the minimum number of right angles there can be?

5. What is the minimum number of acute angles there can be?

6. What is the minimum number of obtuse angles there can be?

7. Each set of numbers below represents the lengths of three line segments.
Which set represent line segments that could be connected to form a triangle? Give the reasoning or show your work to support your choice:

A. (1, 2, 3)
B. (3, 4, 5)
C.(1, 10, 100)
D. (1, 2, 5)
E. (1, 3, 4)
F. (1, 20, 100)

8. Each set of numbers below represents the lengths of three line segments.
Which set represent line segments that could be connected to form a triangle? Give the reasoning or show your work to support your choice

A. (3, 5, 7)
B. (3, 4, 8)
C.(1, 4, 6)
D. (1, 3, 5)
E. (5, 6, 11)
F. (1, 10, 20)

9. Each set of numbers below represents the lengths of three line segments.
Which set represent line segments that could be connected to form a triangle?  Give the reasoning or show your work to support your choice

A. (2, 2, 5)
B. (5, 4, 1)
C.(5, 10, 15)
D. (7, 10, 16)
E. (2, 3, 5)
F. (5, 10, 25)

10. Each set of numbers below represents the lengths of three line segments.
Which set represent line segments that could be connected to form a triangle?  Give the reasoning or show your work to support your choice

A. (3, 1, 2)
B. (3, 2, 5)
C.(1, 15, 100)
D. (40, 5, 40)
E. (30, 4, 10)
F. (20, 30, 50)

11. Each set of numbers below represents the measures of three angles.
Which set represent angle measures that could be found in a triangle?  Give the reasoning or show your work to support your choice

A. (30o, 40o, 30o)
B. (42o, 18o, 130o)
C.(10o, 15o, 100o)
D. (40o, 5o, 40o)
E. (60o, 45o, 75o)
F. (20o, 40o, 50o)

12. Each set of numbers below represents the measures of three angles.
Which set represent angle measures that could be found in a triangle?  Give the reasoning or show your work to support your choice

A. (30o, 100o, 20o)
B. (36o, 42o, 65o)
C.(30o, 57o, 30o)
D. (44o, 63o, 73o)
E. (67o, 41o, 62o)
F. (29o, 131o, 40o)

13. I have a triangle with sides of 3, 4, and 5, and angles of 30o and 60o. Which of the following would be congruent to it? (You will need to use what you've learned about triangles and angle / side relations, as well as your knowledge of the rules of congruence to fill in the gaps and answer the question. Sketches may be helpful.) Give the reasoning or show your work to support your choice:

A. a triangle with angles of 30o, 60o, and 90o
B. an angle of 90o
C.a triangle with sides of 6, 8, and 10
D. a triangle with sides of 3 and 4
E. a triangle with a side measuring 4, next an angle of 90o, and next a side measuring 3
F. a triangle with a side measuring 3, next an angle of 60o, and next a side measuring 4

.

14. I have a triangle with sides of 1 and a side of SQRT(2), with an angle of 45o and an angle of 90o. Which of the following would be congruent to it? (You will need to use what you've learned about triangles and angle / side relations, as well as your knowledge of the rules of congruence to fill in the gaps and answer the question. Sketches may be helpful.). Give the reasoning or show your work to support your choice

A. a triangle with a side of 1, then an angle of 90o, and a side of 1
B. a triangle with a side of 1, then an angle of 90o, then a side of SQRT(2)
C.a triangle with the angles 45o, 45o, 90o
D. a triangle with sides of 1 and 1
E. a triangle with a side of 1, then an angle of 45o, then a side of 1
F. a triangle with an angle of 90o, then a side of SQRT(2), then an angle of 45o

.

15. Which of the following polygons are congruent?

16. Which of the following shapes are congruent?

17. We are trying to measure the height of a building. We have a 1-meter long stick. When we set it on the ground, its shadow is 3 meters long. When we measure the shadow of the building, it is 57 meters long. How high is the building?

18. I can look out my window and see the top of a television transmitter tower. On the map, I see that it is 2 miles away. I read somewhere that the tower is 500 feet tall. As I look at the tower, I see that the very top leaves of a tree sometimes get in the way of the top of the tower. The tree is 50 yards from where I sit. How tall is the tree?

19. Here are two triangles. I am trying to measure the area of triangle ABC. The formula for area of a triangle is

base*height/2.

I know the base, but I need to find the height. I know the top of triangle ABC is directly above a point 4.5 units from point A. I also know that

What is the triangle's height?

20. The sun is shining and I am on a hill. I want to measure the height of a tree downhill from me, using my one-meter stick, and a tape measure for measuring shadows. What do I do to take the slope of the hill into account?

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## #2 2017-05-11 05:23:21

bob bundy
Registered: 2010-06-20
Posts: 8,139

hi taylorn5683

http://www.mathisfunforum.com/viewtopic.php?id=14654

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #3 2017-05-11 14:51:40

taylorn5683
Member
Registered: 2017-02-01
Posts: 10

No I am sorry I did Not but now that I have, I really need help I have been stuck on this for a while and I just don't Understand I a work a Full time job and I have tried to work on it but I need some help Because I havent been haveing as much time to think about it. So if you don't mind helping me I would appericate it. I will work with you to help figure out the answers.
Thank you.

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## #4 2017-05-11 21:09:35

bob bundy
Registered: 2010-06-20
Posts: 8,139

hi taylorn5683

Let's proceed with a few questions at a time.

Questions 1 to 6 are all about what possible triangles you can make.  I assume you know that the angle sum is always 180 and that sets the limits.  eg.  You couldn't have two 90s because there's nothing left for the third angle.  If you drew a base line and made angles of 90 at each end, the next two 'sides' would be parallel and so you'd never get to the vertex of the triangle.

If you try drawing some triangles with one, two and three acute angles, and also with one, two and three obtuse angles you'll soon see what is possible and what just will not make a sensible triangle.

The next questions are all about something called the triangle inequality: http://www.mathsisfun.com/geometry/tria … eorem.html

7E for example won't make a triangle because 1+3 = 4.  If you made a base of 4 and then tried to get a line of 1 and a line of 3 to find a vertex, those lines would meet on the base so you'd just have a line with a point 1 from an end and 3 from the other.  No triangle.  The webpage is interactive; so you can try out different size triangles just by moving the points.  The lengths are initially 2 or 3 digits and your questions only have relatively small numbers, but you could always scale everything up by a factor of 10.  If you can make a x10 triangle, then you can make a x1 triangle with the same (proportionate) lengths.

If you would like me to check your answers, I will, but please post back like this:

Question followed by your answer, so I don't have to keep scrolling back to the first post.

Once we have sorted this worksheet, I'll look at the others.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #5 2017-06-13 14:36:46

taylorn5683
Member
Registered: 2017-02-01
Posts: 10