Triangle Proportionality and Parallel Lines

The video tutorial covers the triangle proportionality theorem, explaining how the ratio of segments in a triangle with parallel lines is equal. It demonstrates the application of this theorem to solve problems and prove line parallelism. The tutorial also includes a step-by-step guide on using cross multiplication to verify the theorem's conditions.

What does the triangle proportionality theorem state?

• The sides of a triangle are always equal.

• The area of a triangle is half the base times the height.

• If a line is parallel to one side of a triangle, it divides the other two sides proportionally.

• The sum of angles in a triangle is 180 degrees.

In the triangle proportionality theorem, what must be true about the lines?

• They must be equal in length.

• They must be parallel.

• They must be perpendicular.

• They must intersect at a point.

What is the first step in setting up a proportion using the triangle proportionality theorem?

• Measure the angles of the triangle.

• Identify the parallel lines.

• Calculate the area of the triangle.

• Find the midpoint of the triangle.

If AB/BC = AD/DE, what can be inferred about the lines in the triangle?

• They are perpendicular.

• They are parallel.

• They are equal in length.

• They form a right angle.

How do you find the length of AD if the whole length is 27 and one part is 9?

• Divide 27 by 9.

• Multiply 9 by 27.

• Subtract 9 from 27.

• Add 9 to 27.

What is the result of applying the theorem to find the length of AD?

• AD is 9.

• AD is 36.

• AD is 18.

• AD is 27.

What mathematical operation is used to prove the lines are parallel?

• Division

• Addition

• Subtraction

• Cross multiplication

What is the value of x if 18 * 1/3 = 9 * x?

• 4/3

• 3/3

• 2/3

• 1/3

How many times does 3 go into 18?

• 8 times

• 6 times

• 7 times

• 5 times

What is the final step in proving the lines are parallel?

• Finding the midpoint

• Cross multiplication

• Calculating the area

• Measuring the angles