Perpendicular and Angle Bisectors

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

Why do we use arcs of the same radius when constructing a perpendicular bisector?

Back

Using arcs of the same radius from each endpoint ensures that the arcs are equidistant from each other, which helps locate the intersection point.

Front

What is the relationship between perpendicular bisectors and triangles?

Back

The perpendicular bisectors of a triangle intersect at a point called the circumcenter, which is equidistant from all three vertices.

Front

Define angle bisector.

Back

An angle bisector is a ray that divides an angle into two equal angles.

Front

What is the significance of the angle bisector in triangles?

Back

The angle bisector of a triangle divides the opposite side into segments that are proportional to the adjacent sides.

Front

How do you find the measure of an angle using an angle bisector?

Back

If you know the measure of the angle, you can divide it by 2 to find the measure of each of the two equal angles created by the bisector.

Front

What is the congruence statement for two triangles that are congruent by the Side-Angle-Side (SAS) postulate?

Back

If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, they are congruent. Example: ΔABC ≅ ΔDEF.

Front

What is the relationship between the angles formed by perpendicular lines?

Back

When two lines intersect perpendicularly, they form four right angles (each measuring 90 degrees).

Front

How do you determine if two triangles are congruent?

Back

Two triangles are congruent if their corresponding sides and angles are equal, which can be established using congruence postulates like SSS, SAS, ASA, AAS, or HL.

Front

What is the formula for finding the length of a segment when given the coordinates of its endpoints?

Back

The length of a segment with endpoints (x1, y1) and (x2, y2) is given by the formula: Length = √((x2 - x1)² + (y2 - y1)²).