Geometric Basics
What are the three undefined terms in geometry?
A: Point, line, plane
What is a conjecture?
A: A statement believed to be true based on observations and patterns.
What is an angle bisector?
A: A line, ray, or segment that divides an angle into two congruent angles.
What is the incenter?
A: The point where the three angle bisectors of a triangle intersect.
What is a perpendicular bisector?
A line that divides a segment into two equal parts and forms a 90° angle.
What is the difference between a line, segment, and ray?
A: A line extends forever in both directions; a segment has two endpoints; a ray has one endpoint and extends forever in one direction.
What is inductive reasoning?
A: Making a generalization based on observations and patterns.
What is the difference between complementary and supplementary angles?
Complementary = 90°; supplementary = 180°.
What is the center of the circle that can be inscribed inside a triangle?
A: The incenter.
What is special about every point on a perpendicular bisector?
A: It is equidistant from the two endpoints of the segment.
What is the minimum number of points needed to determine a line? A plane?
A: 2 points for a line; 3 noncollinear points for a plane.
Find the next number: 1, 1, 2, 3, 5, 8, ___
A: 13
Two angles are complementary. One measures 35°. What is the other angle?
A: 55°
A circular window must touch all three sides of a triangular wall. Which point should be located?
A: The incenter.
What is the circumcenter?
The point where the three perpendicular bisectors of a triangle's sides intersect.
If three points are coplanar, are they always collinear?
A: No. They can be in the same plane without being on the same line.
A sequence is 2, 4, 6, 8, … What are the next two numbers and the rule?
10, 12; add 2 each time.
Two angles are complementary: (3x + 5)° and (2x − 15)°. Find x.
x = 20
What is special about every point on an angle bisector?
A: It is equidistant from the two sides of the angle.
Is the circumcenter always inside a triangle?
No. It can be inside, on, or outside, depending on the triangle.
What is the greatest number of unique rays that can contain a point when several lines pass through that point?
A: Each line through the point creates 2 rays.
A sequence is 128, 64, 32, 16, ___ . What is the next number and rule?
A: 8; divide by 2 each time.
The supplement of an angle is 12 more than twice the angle. Find both angles.
A: 56° and 124°.
Explain why the incenter is the center of an inscribed circle.
A: It is equidistant from all three sides, allowing a circle centered there to touch all three sides.
If a point P is the same distance from points L and C, what line must P lie on?
The perpendicular bisector of segment LC.