Akshay Khanna
12/8/2014 08:49:02 am
In an isosceles triangle since the two side lengths are congruent then the two base angles are congruent. Also in an equilateral triangle since all sides are the same length all angles have the same measure. In a scalene triangle since all the sides have different measures then then all of the angles have different measures.
Hardik Veguru
12/8/2014 09:21:19 am
To classify triangles with "a,b and c" being one leg/side:
priyan
12/8/2014 10:16:11 am
a right or obtuse triangle may be scalene or iscoles but not equilatteral
Franklin
12/8/2014 10:26:36 am
The longest side of a triangle is always opposite to the angle with the largest measure. The shortest side of a triangle is always opposite to the angle with the shortest angle measure.
Vedika
12/8/2014 11:41:04 am
If a triangle has two congruent sides, the remaining side would be called the base, and base angles would be congruent.
Pranav the Swagger
12/9/2014 05:35:06 am
I guess most of the relationships are taken. Today's lesson also corresponds with the Law of Sines: sin<A / BC = sin<B / AC = sin<C / AB
Avi Sura
12/9/2014 05:54:08 am
Practically all of the answers possible are already there so I am just going to summarize them.
Akhil
12/9/2014 05:57:04 am
The angle measure is directly proportional to the side length. If the angle measure is larger than the angle measure of another angle in the triangle, then the non-adjacent side would be larger than the non-adjacent side of the other angle. In the same way, if the angle measures are congruent, then the non-adjacent sides will also be congruent.
Shivam
12/9/2014 06:03:01 am
Basically, an angle's measure determines the side length. If an angle has the smallest measure, then the side opposite to that angle is the shortest side, and the same with all the other angle measures. This "method" can also be used with the side's length and the angle opposite to it.
Aarushi
12/9/2014 06:08:24 am
It seems like everyone who answered so far already included all the possible answers that I know of. Personally, I think the relationship between angles and sides is best explained through the Pythagorean Theorem:
Sanjana
12/9/2014 06:14:25 am
All the angles in a triangle has to equal to 180 degrees and each angle has an opposite side whose length depends on the angle measure. Additionally, when two sides are added together, the sum must be larger than the third side. this does not always happen for the angles: 100 degrees, 40 degrees, 40 degrees.
diana d'souza
12/9/2014 06:39:46 am
the following can be used to determine the relationship between side lengths and angles:
Aashvi
12/9/2014 06:55:46 am
After discussing lesson 5-3 in class, I learned that there is a relationship between the angle measures and side lengths of a triangle. The longest side of a triangle always has the largest angle opposite to it, and the shortest side of a triangle always has the smallest angle opposite to it. This can also be switched around, such as the largest angle always has the longest side opposite to it, and the smallest angle always has the shortest side opposite to it. This shows the relationship between the sides lengths and angle measures of a triangle.
Andrew
12/9/2014 06:56:21 am
The longest side of the opposite angle is the biggest angle. The shortest side of the opposite angle is the smaller side. The angle measures can be determined by using the Pythagorean Theorem.
Anna Jiang
12/9/2014 07:20:44 am
so basically every relationship between angle measures and side lengths is already posted .-.
Karan M
12/9/2014 11:43:11 pm
One mathematical theorem that defines the relationship between angles and sides states that the smallest angle is always opposite the shortest side, and the longest side is always opposite the largest angle. In the same way, the 2nd longest side will be opposite the 2nd largest angle.
Calvin Li
12/10/2014 11:11:10 am
The relative measure of an angle corresponds to its opposite side. In this same way, congruency between the measures of the angles of a triangle also apply to its opposite sides. For example, in a triangle like this:
Calvin Li
12/10/2014 11:14:48 am
Well, that triangle didn't turn out so well.
Hrishi
12/10/2014 11:46:13 am
As others have stated as well, almost all of the possibilities to describe the angle to side relationships have been given. I will just summarize and provide an example.
Anika
12/11/2014 07:15:17 am
1. Scalene triangles have three different angle measures and three different side lengths
Sachika shah
12/11/2014 12:03:25 pm
the longest side is always opposite to the largest angle as others have stated in a right triangle the hypotenuse is the longest side which is always opposite to the right angle which is the largest angle.
Swathi
12/12/2014 06:23:00 am
if the triangle has two congruent sides, then the angles opposite from the congruent sides are also congruent. if the triangle has one right angle, then the side opposite from the right angle, or the hypotenuse is the longest. if the triangle has no sides that are congruent to another side, and is scalene, then the side opposite from the greatest angle is the longest side. the second greatest angle is opposite from the second largest side, and it is the same for the shortest side.
Nitish Nimma
12/12/2014 06:40:56 am
According to the angle suk theoren or the corresponding angles theorem, the angle that corresponds to the largest side is the largest angle, and so on in that order. The side lenghts have relevance to the angle lenghts too. Comments are closed.
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