Question on Triangles and the lines intersecting through it

In summary, the problem involves a triangle ABC where points L and M divide the sides AB and BC in the ratio 2:3 respectively. Point P is formed by the intersection of AM and LC. A line parallel to BA is drawn from point P, intersecting at D. The task is to find the ratio of AD to DC. The problem also suggests constructing a triangle and measuring to make progress.
  • #1
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Homework Statement



In triangle ABC, point L and M divides the sides AB and BC in the ratio 2:3 respectively. AM and LC intersect at point P. From point P a line parallel to BA is drawn intersecting at D. Find the ratio of AD:DC

The Attempt at a Solution



I have attached the picture of the triangle which is all I could make from the question. Please help me out
 

Attachments

  • TRIANGLE 1.JPG
    TRIANGLE 1.JPG
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  • #2
Please show your best attempt at the problem.
This helps us to best help you.

In triangle ABC, point L and M divides the sides AB and BC in the ratio 2:3 respectively.
"respectively" does not mean anything here.

Do you mean that |BL|/2=|LA|/3 and |BM|/2 = |MC|/3 or what?
Is ABC a scalene triangle?

Note: you can probably make headway just by carefully constructing a triangle and measuring.
You certainly want a sketch that better represents the situation.
 

Related to Question on Triangles and the lines intersecting through it

1. What is a triangle?

A triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry and is often used in mathematical and scientific applications.

2. What are the types of triangles?

There are three types of triangles based on the length of their sides: equilateral, isosceles, and scalene. Triangles can also be classified based on the measure of their angles: acute, right, and obtuse.

3. What is the Pythagorean Theorem?

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. It can be written as a² + b² = c², where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

4. How do you find the area of a triangle?

The area of a triangle can be found by using the formula A = 1/2 * base * height, where A is the area, the base is the length of one side of the triangle, and the height is the perpendicular distance from the base to the opposite vertex.

5. How do you solve for unknown angles in a triangle?

In a triangle, the sum of all three angles is always 180 degrees. To solve for an unknown angle, you can subtract the known angles from 180 degrees. You can also use the properties of similar triangles or the law of sines and cosines to solve for unknown angles.

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