Point-Line Distance and Angle Bisectors in Geometry

What is the shortest distance between a point and a line?

• The distance along any segment

• The distance along the line

• The perpendicular distance

• The distance along the hypotenuse

Why is the perpendicular distance the shortest distance between a point and a line?

• Because it forms a right triangle

• Because it is the longest side of the triangle

• Because it is the hypotenuse

• Because it is the only distance that can be measured

What does an angle bisector do?

• Splits a triangle into two equal triangles

• Splits a line into two equal segments

• Splits an angle into two equal angles

• Splits an angle into two unequal angles

If a point lies on an angle bisector, what can be said about its distance from the sides of the angle?

• It is not related to the sides

• It is equidistant from the sides

• It is farther from one side than the other

• It is closer to one side than the other

What is the relationship between two right triangles formed by a point on an angle bisector?

• They are not related

• They are congruent

• They are similar

• They are different

What can be concluded if a point is equidistant from the sides of an angle?

• It lies on one of the sides

• It lies outside the angle

• It lies on the angle bisector

• It lies on the vertex of the angle

Which theorem can be used to prove the congruency of two right triangles?

• Angle-Side-Angle (ASA)

• Side-Angle-Side (SAS)

• Side-Side-Side (SSS)

• Pythagorean Theorem

What is the significance of the hypotenuse in the context of right triangles formed by a point on an angle bisector?

• It is the shortest side

• It is the longest side

• It is equal to the other sides

• It is not related to the other sides

What does the RSH case stand for in proving triangle congruency?

• Right-Side-Side

• Right-Hypotenuse-Side

• Right-Side-Hypotenuse

• Right-Angle-Side

What is the result if two triangles are congruent?

• Their corresponding sides are different

• Their corresponding angles are different

• Their corresponding angles and sides are congruent

• Their corresponding hypotenuses are different