Triangle Theorems and Proportions

The video tutorial covers proportions in triangles, focusing on the Side Splitter Theorem, Triangle Midsegment Theorem, and Triangle Angle Bisector Theorem. It includes examples demonstrating how to apply these theorems to solve problems involving parallel lines and proportional segments. The tutorial also introduces a corollary to the Side Splitter Theorem, explaining the proportionality of segments when three parallel lines intersect two transversals.

What does the Side Splitter Theorem state?

• If a triangle has three equal sides, it is called an equilateral triangle.

• If a triangle has two equal sides, the angles opposite those sides are also equal.

• If a line bisects an angle of a triangle, it divides the opposite side into two segments that are proportional to the other two sides.

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

According to the Triangle Midsegment Theorem, if a segment joins the midpoints of two sides of a triangle, what can be said about this segment?

• It is parallel to the third side and half as long.

• It is perpendicular to the third side and twice as long.

• It is parallel to the third side and equal in length.

• It is perpendicular to the third side and half as long.

In the example with triangle JLN, if LN equals 9.6, what is the length of LM?

• 6

• 9.6

• 3.6

• 5

How do you verify if the sides of a triangle are divided proportionally?

• By comparing the ratios of the corresponding segments.

• By measuring the angles of the triangle.

• By calculating the area of the triangle.

• By checking if the triangle is equilateral.

Using the Side Splitter Theorem, if PS = x + 2 and SQ = 16, what is the value of x if RT = x and TQ = 12?

• 4

• 10

• 6

• 8

What does the corollary to the Side Splitter Theorem state about three parallel lines intersecting two transversals?

• The segments are perpendicular.

• The segments are equal.

• The segments are proportional.

• The segments are congruent.

According to the Triangle Angle Bisector Theorem, if a ray bisects an angle of a triangle, what is true about the opposite side?

• It is divided into two segments that are proportional to the other two sides.

• It is divided into two equal segments.

• It is divided into two segments that are perpendicular to the other two sides.

• It is divided into two segments that are congruent to the other two sides.

In the example using the Triangle Angle Bisector Theorem, if AD = x and AC = 13, what is the length of CD?

• 13 - x

• x + 13

• x - 13

• 13 + x

If AB = 10 and CB = 16, what is the proportion used to find the value of x in the Triangle Angle Bisector Theorem example?

• AD/CD = AB/CB

• AD/CD = CB/AB

• AB/AD = CD/CB

• AB/CD = AD/CB

What is the value of x if 16x = 130 - 10x?

• 8

• 5

• 6

• 7