Questions and Answers
What does the Linear Pair Conjecture state?
According to the Vertical Angle Conjecture, what can be said about two vertical angles?
What does the Corresponding Angle Conjecture state?
What can be said about alternate interior angles when two parallel lines are cut by a transversal?
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What does the Perpendicular Bisector Conjecture state?
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If a point is equidistant from the endpoints of a segment, what can be said about that point?
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According to the Shortest Distance Conjecture, what is the shortest distance from a point to a line measured along?
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What do the three angle bisectors of a triangle converge at according to the Angle Bisector Concurrency Conjecture?
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What does the Triangle Sum Conjecture state about the measures of the angles in a triangle?
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According to the Isosceles Triangle Conjecture, what can be inferred if a triangle is isosceles?
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What does the Side-Angle Conjecture state?
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Study Notes
Geometric Conjectures
- Linear Pair Conjecture: The sum of angles forming a linear pair is always 180º.
- Vertical Angle Conjecture: Vertical angles are always congruent (equal in measure).
- Corresponding Angle Conjecture: When parallel lines are intersected by a transversal, corresponding angles are congruent.
- Alternate Interior Angle Conjecture: If two parallel lines are cut by a transversal, their alternate interior angles are congruent.
- Alternate Exterior Angles Conjecture: Alternate exterior angles are congruent when parallel lines are cut by a transversal.
- Parallel Lines Conjecture: Cutting parallel lines with a transversal results in congruent corresponding, alternate interior, and alternate exterior angles.
- Converse of Parallel Lines Conjecture: If a transversal creates pairs of congruent corresponding angles, alternate interior angles, or alternate exterior angles, the lines are parallel.
- Perpendicular Bisector Conjecture: A point on the perpendicular bisector of a segment is equidistant from the segment's endpoints.
- Converse of Perpendicular Bisector Conjecture: A point equidistant from the endpoints of a segment lies on its perpendicular bisector.
- Shortest Distance Conjecture: The shortest distance from a point to a line is along the perpendicular segment to the line.
- Angle Bisector Conjecture: A point on an angle bisector is equidistant from the sides of the angle.
- Angle Bisector Concurrency Conjecture: The three angle bisectors of a triangle intersect at the incenter.
- Perpendicular Bisector Concurrency Conjecture: The three perpendicular bisectors of a triangle intersect at the circumcenter.
- Altitude Concurrency Conjecture: The three altitudes of a triangle are concurrent at the orthocenter.
- Circumcenter Conjecture: The circumcenter is equidistant from the triangle's vertices.
- Incenter Conjecture: The incenter is equidistant from the sides of the triangle.
- Median Concurrency Conjecture: The three medians of a triangle are concurrent at the centroid.
- Centroid Conjecture: The centroid divides each median such that the distance from the centroid to the vertex is twice that to the midpoint of the opposite side.
- Center of Gravity Conjecture: The centroid acts as the center of gravity for the triangle's region.
- Triangle Sum Conjecture: The angles of a triangle always add up to 180°.
- Third Angle Conjecture: If two angles of one triangle are equal to two angles of another, their third angles are also equal.
- Isosceles Triangle Conjecture: In an isosceles triangle, the base angles are congruent.
- Converse of the Isosceles Triangle Conjecture: Congruent base angles imply that the triangle is isosceles.
- Triangle Inequality Conjecture: The sum of any two sides of a triangle must be greater than the length of the third side.
- Side-Angle Conjecture: In a triangle, a longer side corresponds to a larger opposite angle.
- Exterior Angle Conjecture: The sum of the exterior angles of any convex polygon is 360 degrees.
- SSS Congruence Conjecture: Triangles are congruent if all three sides of one triangle are equal to those of another.
- SAS Congruence Conjecture: Triangles are congruent if two sides and the included angle of one triangle are congruent to another.
- ASA Congruence Conjecture: Two angles and the included side of one triangle congruent to another also indicate triangle congruence.
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Description
Test your understanding of essential geometry conjectures with this flashcard quiz. It covers key concepts such as linear pairs, vertical angles, and corresponding angles. Perfect for reviewing before your final exam!
