Triangle rules and theorems allow us to understand the properties of this shape. As among the most central elements of trigonometry, triangle have countless geometric rules. Among other things, these help us to distinguish right triangles from equilateral triangles and isosceles triangles.

You are watching: How do you find the value of x in a triangle

Let"s review some the the many notable trigonometric triangle rules.

### Interior angles Rule

The internal angles rule states that the 3 angles that a triangle must equal 180°. As you can see below, the 3 angle measurements of obtuse triangle ABC add to 180°. ### Sides of a Triangle

The sides of a triangle preeminence asserts the the sum of the lengths of any kind of two sides of a triangle needs to be greater than the size of the third side. Watch the next lengths that the acute triangle below. The sum of the lengths the the two shortest sides, 6 and 7, is 13. That length is higher than the size of the longest side, 8. ## Triangle Congruence Rules

Congruent triangles space triangles whose matching sides and also angles are equal. In trigonometric fashion, equal sides and equal angles room proven congruent v the four triangle rules of congruence. We’ll go with these one in ~ a time.

### #1: SSS Rule

The side-side-side (SSS) dominance says that once the 3 side measurements of a triangle complement the 3 side measurements of another triangle, this two forms are congruent.

See the right-angled triangles below. The political parties of the triangle DEF are the same precise lengths as triangle GHI, making them congruent. ### #2: ASA Rule

The angle-side-angle (ASA) rule states that as soon as two angles and one side of a triangle space equal to that of an additional triangle, they space congruent triangles.

See triangle JKL and MNO. Angles J and M, K and N (the opposite angle to the size of the hypotenuse), and the hypotenuse-legs the both triangles space all equal. Therefore, triangles JKL and also MNO are congruent. ### #3: AAS Rule

The angle-angle-side (AAS) dominance asserts that as soon as two triangles have actually the following corresponding properties, they should be congruent:

Two angles One the contrary side size with no vertices

### #4: SAS Rule

The side-angle-side (SAS) preeminence states that if the included angle and also the two consisted of side lengths of a triangle space equal to that of an additional triangle, climate the two space congruent. See below triangles CDE and also FGH. Right angle C and angle F, the length of d and g, and the hypotenuse size of c and also f are equal. Therefore, triangle CDE=FGH.

See more: How Long Are Rounds In Boxing Round? The Distance (Boxing) ## The prestige of Triangle Rules

Expanding your knowledge of triangle rules will make it less complicated to find out other trigonometric ideas like Pythagoras theorem and cosine, tangent, and sine rules. This understanding will also aid you understand the area of a triangle and polygon.