# If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides ____________________.

Question
If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides ____________________.

2020-12-25
This is the Triangle Proportionality Theorem:
If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides proportionally.

### Relevant Questions

The converse of the Pythagorean theorem is also a true statement: If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle. Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle.
(-4,3), (0,5), and (3,-4)
The converse of the Pythagorean theorem is also a true statement: If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle. Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle.
(-3,1), (2,-1), and (6,9)
The converse of the Pythagorean theorem is also a true statement: If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle. Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle.
(-3,1), (2,-1), and (6,9)
The converse of the Pythagorean theorem is also a true statement: If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle. Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle.
(-3,1), (2,-1), and (6,9)
The converse of the Pythagorean theorem is also a true statement: If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle. Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle.
(-4,3), (0,5), and (3,-4)
Aidan knows that the observation deck on the Vancouver Lookout is 130 m above the ground. He measures the angle between the ground and his line of sight to the observation deck as $$\displaystyle{77}^{\circ}$$. How far is Aidan from the base of the Lookout to the nearest metre?
Two light sources of identical strength are placed 8 m apart. An object is to be placed at a point P on a line ? parallel to the line joining the light sources and at a distance d meters from it (see the figure). We want to locate P on ? so that the intensity of illumination is minimized. We need to use the fact that the intensity of illumination for a single source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source.
$$\displaystyle{8}\frac{{3}}{{4}}{c}{m}$$
An electron is fired at a speed of $$\displaystyle{v}_{{0}}={5.6}\times{10}^{{6}}$$ m/s and at an angle of $$\displaystyle\theta_{{0}}=–{45}^{\circ}$$ between two parallel conductingplates that are D=2.0 mm apart, as in Figure. Ifthe potential difference between the plates is $$\displaystyle\triangle{V}={100}\ {V}$$, determine (a) how close d the electron will get to the bottom plate and (b) where the electron will strike the top plate.