0
Why is the sum of a triangle's angles will always equal 180 degrees?
Wiki User
∙ 15y ago
By historical convention a complete circle is 360 degrees, so if you take a point on a straight line and rotate until you face the other way the total angle is 180 degrees.
Now if you take any two parallel lines, any distance apart, and mark a point anywhere on one line, and two points anywhere on the other line, then by varying these two lines and three points you can form any shaped triangle by joining up the three points.
Now because the lines are parallel there is no angle between them, so a straight line drawn from one to the other will provide two identical angles rotated 180 degrees about.
Call these two identical angles A. Now if you take a new line from one of the intersections to a new point on the other parallel line the same applies and we will call the two new identical angles B.
If you draw this out you will have a triangle with a base with angles A & B and for the sake of convention we will call the remaining angle at the peak of the triangle C.
The total angle at the peak of the triangle enabling one of the parallel lines to rotate and face the other way is, as we have said, 180 degrees but is also equal to C plus the rotated angles A and B. therefore A+B+C = 180 Degrees which is the same as your three angles in the triangle. ( It's much easier with diagrams). Or, you can work simpler like this: In a piece of paper draw a conveniently large scalene triangle ABC. Write 1 under the vertex A, 2 under the vertex B, and 3 under the vertex C (these numbers represent respectively the measure of angles A, B, and C).
Cut the paper, and on another piece of paper point the three vertices A, B, and C. Connect these three points, and write the corresponding numbers 1, 2, and 3 respectively at vertices A, B, and C.
Take the triangle and put the vertex C at the point A, A at C, and point B. Connect point B with others, and write the corresponding numbers under the corresponding vertices.
Take the triangle and put the vertex C at the point B, the vertex B at A, and point A. Connect point A with others, and write the corresponding numbers under the corresponding vertices again.
You can see that a straight angle is formed, whose measure is equal to the sum of the angles 1 + 3 + 2. Since the measure of a straight angle is equal to 180 degrees, then we say that the sum of the angles of a triangle is eaqual to 180 degrees
(m A = 1) + (m B = 2) + (m C = 3) = 180 degrees.
Wiki User
∙ 15y ago
Add your answer:
Earn +20 pts
In the two triangles all angles equal 60 degrees and AB equals EF Are the two triangles congruent?
Yes
The triangles sum says that the 3 angle in a triangle always equal 180?
The three angles of a triangle are always equal to 180°, if not equal to 180° then it is not a triangle.
What are a score or more facts about the properties of angles and triangles?
1 Angles are measured in degrees, minutes and seconds 2 Angles greater than 0 but less than 90 degrees are acute 3 Angles of 90 degrees are right angles 4 Angles greater the 90 but less than 180 degrees are obtuse 5 Angles greater than 180 but less than 360 degrees are reflex 6 Angle of 360 degrees is a full rotation 7 Triangles are 3 sided polygons 8 Triangles have 3 inside angles that add up to 180 degrees 9 Triangles have 3 outside angles that add up to 360 degrees 10 Triangle that is scalene has 3 different acute angles 11 Triangle that is a right angle triangle has a 90 degree angle and 2 acute angles 12 Triangle that is obtuse has 1 obtuse angle and 2 acute angles 13 Triangle that is isosceles has 2 equal base angles and 2 equal sides 14 Triangle that is equilateral has 3 equal inside angles and 3 equal sides 15 Triangles have no diagonals 16 Triangles will tessellate leaving no gaps or overlaps 17 Triangle's area is 0.5*base*perpendicular height 18 Triangle's perimeter is the sum of its 3 sides 19 Triangle as a right angle triangle is subject to Pythagoras' theorem 20 Triangles are subject to the rules of trigonometry 21 Triangles are the corner stones of all other polygons
With similar triangles the corresponding angles are equal True or False?
True. With similar triangles the corresponding angles are equal.
Is it true that all triangles have at least 2 acute angles?
Yes. The total degrees of the 3 angles in a triangle must equal 180, so it's not possible to have a triangle with 2 angles >= 90.
What is true about the angles and sides on similar triangles?
All the Angles and sides on Triangles are always going to equal 180 Degrees
Sum of the angles of a triangles?
The sum of the 3 angles of a triangle will ALWAYS equal 180 degrees.
Triangle has no equal anles or sides?
Equaliateral Triangles have all three sides and angles (60 degrees)equal Isosceles Triangles have to equal sides and angles Scalene Triangles have no equal sides or angles
This sort of triangle has three equal sides and three equal angles?
Equilateral triangles have three equal sides and three equal angles. By definition, the angles must always measure 60 degrees each.
Does an equallaterail triangle equal 360 degrees?
No. The sum of the angles in ALL triangles is equal to 180 degrees. No triangle's angles equal 360.
Are the angles of similar triangles always equal?
The relative angles are congruent
What is an isosceles triangle measure up to?
In all triangles, the angles always measure up 180 degrees. In an isosceles triangle two of the angles are equal.
Do some equilaterall triangles have angles?
All equilateral triangles have 3 equal interior angles each measuring 60 degrees
What is the classification or triangles by side and angles?
An equilateral triangle is one where all sides are of equal length and all internal angles are 60 degrees. An isosceles triangle is one where 2 adjacent angles are of equal size and 2 adjacent sides are of equal length. A scalar triangle is one where no sides are equal in length and no angles are equal in size. A right-angled triangle is one where one of the internal angles is 90 degrees. The internal angles of all triangles always add up to 180 degrees.
How are isoseles triangles and equilateral trangles alike and different?
They are both triangles that have interior degrees of 180 and exterior degrees of 360. An equilateral has three equal sides and three equal angles. An isosceles has two equal sides and two equal angles.
Is an equilateral triangle acute triangle?
Equilateral triangles are equal at all sides which means that all angles well always be 60 degrees
Do all triangles have an acute angle?
All triangles have at least 2 acute angles. All 3 angles of a triangle will equal 180 degrees.
