# What does it mean if two lines are parallel in a triangle?

## What does it mean if two lines are parallel in a triangle?

If a line intersects two sides of a triangle and splits those sides in equal proportions, then that line must be parallel to the third side of the triangle.

### How do you find the angle between parallel lines?

Formulas for Angle Between Two Lines The angle between two lines, of which one of the line is y = mx + c and the other line is the x-axis, is θ = Tan-1m. The angle between two lines that are parallel to each other and having equal slopes (m1=m2 m 1 = m 2 ) is 0º.

**What do angles on a parallel line add up to?**

Co-interior angles on the same side of an intersecting transversal add to 18 0 o 180^o 180o. We can often spot interior co-interior angles by drawing a C shape.

**How do you work out the missing side of a triangle?**

Given two sides

- if leg a is the missing side, then transform the equation to the form when a is on one side, and take a square root: a = √(c² – b²)
- if leg b is unknown, then. b = √(c² – a²)
- for hypotenuse c missing, the formula is. c = √(a² + b²)

## What is the three parallels theorem?

Three Parallel Lines Theorem If three parallel lines intersect two transversals, then they divide the transversals proportionally.

### What do angles on parallel lines add up to?

**What are the rules for parallel line angles?**

There are 3 main rules:

- Corresponding angles are equal. A line cutting across two parallel lines creates four pairs of equal corresponding angles, as in the diagram below:
- Alternate angles are equal.
- Co-interior angles add to 180°
- Vertically opposite angles are equal.
- Angles on a line add to 180°

**How do I find the third side of a triangle?**

Different Ways to Find the Third Side of a Triangle For a right triangle, use the Pythagorean Theorem. For an isosceles triangle, use the area formula for an isosceles. If you know some of the angles and other side lengths, use the law of cosines or the law of sines.

## What is the side splitter theorem?

Side-Splitter Theorem If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

### How do you use three parallel lines theorem?

If a line divides two sides of a triangle proportionally, then it is parallel to the third side. If three parallel lines intersect two transversals, then they divide the transversals proportionally.

**What is the equation for parallel lines?**

In a linear equation of the form y=mx+b, parallel lines will always have the same m.

**How do I calculate the sides of a triangle?**

Given angle and hypotenuse Apply the law of sines or trigonometry to find the right triangle side lengths: a = c * sin(α) or a = c * cos(β) b = c * sin(β) or b = c * cos(α)

## What formula should be used to find the length of the third side?

You can use the Pythagorean Theorem to find the length of the hypotenuse of a right triangle if you know the length of the triangle’s other two sides, called the legs. Put another way, if you know the lengths of a and b, you can find c.

### How do I find the length of the sides of a triangle?

The Law of Sines says that for all angles of a triangle, the ratio of the sine of that angle to its opposite side will always be the same. The length of side c is 2.98. The Law of Cosines says you can determine the length of any triangle side if you know its opposite angle and the lengths of the other two sides.