How do I figure out this question? Is there a formula I need?
For which of the following sets of line segments is it possible to consturct a triangle?
1. Sides of length 17cm, 18 cm,and19 cm
2. Sides of length 11m, 18m, and 6 m
3. Sides of length 46ft, 25ft,and70ft
No side can be greater than the sum of the other two sides.
So that means none of these can construct a triangle then.
relook at 1. Is any side greater than the sum of the two others? What about 3?
1. no
2. yes
3. no
I am still kinda of confused on this.
Suppose you want to draw a triangle with sides 10, 3, and 5
first draw a base 10 cm long.
Now set a compass at 5 cm and and with its centre at the end of the line, draw an arc above the line.
Change the radius of your compass to 3 cm, set the centre of the compass at the end of the line and draw another arc above the line.
The intersection of these two arcs will be the third vertex of your triangle.
BUT in the case I gave you those two arcs never meet, so no triangle is possible
This shows the principle that "bobpursely" stated for you.
TO HAVE A TRIANGLE, THE SUM OF ANY OF THE TWO SIDES MUST BE GREATER THAN THE THIRD SIDE
measure and state the size of angle mn
To figure out if it is possible to construct a triangle, you need to follow a basic rule for triangles known as the Triangle Inequality Theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side.
So, for each set of line segments given, you need to check if any side is greater than the sum of the other two sides. If this condition is not met for any of the sides, then it is not possible to construct a triangle with those lengths.
Let's go through the sets one by one:
1. Sides of length 17cm, 18 cm, and 19 cm
To check if a triangle can be formed, compare each side with the sum of the other two sides:
- Side of length 17 cm: (18 cm + 19 cm) > 17 cm is True
- Side of length 18 cm: (17 cm + 19 cm) > 18 cm is True
- Side of length 19 cm: (17 cm + 18 cm) > 19 cm is True
In this case, all three sides satisfy the Triangle Inequality Theorem, so it is possible to construct a triangle with side lengths of 17 cm, 18 cm, and 19 cm.
2. Sides of length 11m, 18m, and 6m
Check the triangle inequality for each side:
- Side of length 11 m: (18 m + 6 m) > 11 m is True
- Side of length 18 m: (11 m + 6 m) > 18 m is True
- Side of length 6 m: (11 m + 18 m) > 6 m is False
In this case, the side of length 6 m does not satisfy the Triangle Inequality Theorem, so it is not possible to construct a triangle with these lengths.
3. Sides of length 46 ft, 25 ft, and 70 ft
Checking the triangle inequality:
- Side of length 46 ft: (25 ft + 70 ft) > 46 ft is True
- Side of length 25 ft: (46 ft + 70 ft) > 25 ft is True
- Side of length 70 ft: (46 ft + 25 ft) > 70 ft is True
In this case, all three sides satisfy the Triangle Inequality Theorem, so it is possible to construct a triangle with side lengths of 46 ft, 25 ft, and 70 ft.
To summarize, for the given sets of line segments:
- Set 1 can form a triangle.
- Set 2 cannot form a triangle.
- Set 3 can form a triangle.
Remember to always check if any side is greater than the sum of the other two sides to determine if a triangle can be constructed.