Exploring Angle Bisectors, Medians, and Altitudes

What does an angle bisector do?

• Cuts an angle into two equal parts

• Connects a vertex to the midpoint of the opposite side

• Forms a 90-degree angle

• Cuts a line segment into two equal parts

Which of the following is true about a median?

• It cuts an angle into two equal parts

• It connects a vertex to the midpoint of the opposite side

• It forms a 90-degree angle

• It creates two congruent angles

What is a key property of an altitude?

• It cuts a line segment into two equal parts

• It cuts an angle into two equal parts

• It forms a 90-degree angle

• It connects a vertex to the midpoint of the opposite side

What does a perpendicular bisector do?

• Forms a 90-degree angle and cuts an angle into two equal parts

• Connects a vertex to the midpoint of the opposite side

• Forms a 90-degree angle and cuts a line segment into two equal parts

• Cuts an angle into two equal parts

If AD is a median of BC, what does it imply?

• AD is perpendicular to BC

• AD cuts an angle into two equal parts

• AD cuts BC into two equal parts

• AD forms a 90-degree angle with BC

If BD is an angle bisector of angle ABC, what does it imply?

• BD forms a 90-degree angle with BC

• BD is perpendicular to BC

• BD cuts BC into two equal parts

• BD cuts angle ABC into two equal parts

If LM is an altitude, what is always true?

• LM cuts a line segment into two equal parts

• LM connects a vertex to the midpoint of the opposite side

• LM forms a 90-degree angle

• LM cuts an angle into two equal parts

If a line is a perpendicular bisector, what does it do?

• Forms a 90-degree angle and cuts a line segment into two equal parts

• Cuts an angle into two equal parts

• Connects a vertex to the midpoint of the opposite side

• Forms a 90-degree angle and cuts an angle into two equal parts

In the problem where AD is a median of BC, what is the value of x if 4x + 9 = 7x - 6?

• x = 3

• x = 9

• x = 5

• x = 7

In the problem where LM is an altitude, what is the value of x if 9x - 9 = 90?

• x = 9

• x = 10

• x = 11

• x = 12