Exploring Angle Bisectors and Proportions

What do angle bisectors do in a triangle?

• They split the angle into two equal parts and divide the triangle proportionally.

• They divide the triangle into two equal areas.

• They only divide the triangle's sides equally.

• They create right angles within the triangle.

Which of the following is a correct proportion setup to find the value of x?

• 4/8 = 6/x

• 4/x = 8/6

• 6/4 = x/8

• x/4 = 8/6

What is the value of x when 4x = 48?

• 12

• 10

• 14

• 16

What is the first step in solving a proportion by cross-multiplying?

• Multiply the denominators.

• Add the numerators.

• Subtract the denominators.

• Multiply the numerator of one fraction by the denominator of the other.

If you start with 8/x, which proportion should you use to remain consistent?

• 4/6

• 6/4

• x/8

• 8/4

Why does the proportion 6/4 = 8/x not work?

• Because 6 and 8 are not equal.

• Because 8 and x are not on the same side.

• Because 6 and 4 are not on the same side.

• Because the proportion is not consistent.

What is the correct proportion setup for 7/13 to find the unknown segment?

• 7/13 = x/15

• 7/13 = 15/x

• 7/13 = (15-x)/x

• 7/13 = x/(15-x)

What is the value of x when 20x = 195?

• 9.25

• 9.50

• 9.75

• 10.00

Which of the following is NOT a step in solving the proportion 7/x = (15-x)/13?

• Subtracting 7x from both sides.

• Adding 13x to both sides.

• Distributing the multiplication over subtraction.

• Cross-multiplying the terms.

What is the purpose of subtracting 15-x in the complex example?

• To find the length of the bisector.

• To find the length of the entire side.

• To find the length of the unknown segment.

• To find the length of the known segment.