Geometry Constructions

Front

What is the construction for a perpendicular through a point NOT on the line?

Back

To construct a perpendicular through a point NOT on the line, place the compass point on the external point and draw an arc that intersects the line at two points. Then, using those intersection points, draw arcs above and below the line. Finally, connect the external point to the intersection of the arcs to form the perpendicular.

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. It can be constructed using a compass and straightedge by drawing arcs from both endpoints of the segment and connecting the intersection points.

Front

How do you construct the bisector of a given angle?

Back

To construct the bisector of a given angle, place the compass point at the vertex of the angle and draw an arc that intersects both rays of the angle. Then, from the intersection points, draw arcs that intersect each other. Finally, connect the vertex to the intersection of the arcs.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they are in the same plane and do not intersect, no matter how far they are extended.

Front

What is the definition of congruent angles?

Back

Congruent angles are angles that have the same measure, regardless of their orientation or position.

Front

What is the construction for a perpendicular to a given line at a point on the line?

Back

To construct a perpendicular to a given line at a point on the line, place the compass point on the point and draw an arc that intersects the line at two points. Then, using those intersection points, draw arcs above and below the line and connect the intersection of the arcs to the original point.

Front

What is the significance of the circumcenter in a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect. It is equidistant from all three vertices of the triangle and is the center of the circumcircle.

Front

What is the difference between similar and congruent figures?

Back

Similar figures have the same shape but may differ in size, while congruent figures have the same shape and size.

Front

How do you identify a right angle using geometric constructions?

Back

A right angle can be identified using a compass and straightedge by constructing a perpendicular line to a given line at a point on that line.

Front

What is the purpose of using a compass in geometric constructions?

Back

A compass is used in geometric constructions to create arcs and circles, which help in measuring distances and creating precise angles.