Geometry Postulates and Theorems Flashcards

Questions and Answers

What does Postulate #1 state?

Through any two points there is exactly one line (correct)

Two points determine a segment

A line has length but no width

Through any two points there is exactly one plane

What is stated in Postulate #2?

If two lines intersect then the intersection is a point.

What does Postulate #3 specify?

If two planes intersect then the intersection is a line.

What is the statement of Postulate #4?

Through any three nonlinear points there is exactly one plane. Signup and view all the answers

What can be measured using a ruler according to the Ruler Postulate?

The distance between two points. Signup and view all the answers

What does the Segment Addition Postulate say?

If there are three collinear points, then the opposite segments create the entire segment. Signup and view all the answers

What is the range for measuring angles using a protractor?

From 0 to 180 degrees. Signup and view all the answers

What does the Angle Addition Postulate state?

Two adjacent angles that share a vertex are the sum of the entire angle. Signup and view all the answers

What can be said about angles that form a linear pair according to the Linear Pair Postulate?

The angles are supplementary. Signup and view all the answers

What does the Vertical Angle Theorem state?

Vertical angles are congruent. Signup and view all the answers

What is the statement of Theorem #1?

All right angles are congruent. Signup and view all the answers

What does Theorem #2 state about angles?

If two angles are congruent and supplementary, then each angle is a right angle. Signup and view all the answers

What can be concluded from the Same Side Interior Angle Theorem?

If a transversal intersects parallel lines, then the same side interior angles are supplementary. Signup and view all the answers

What does the Alternate Interior Angle Theorem state?

If a transversal intersects parallel lines, then the alternate interior angles are congruent. Signup and view all the answers

What is claimed by the Alternate Exterior Angle Theorem?

If a transversal intersects parallel lines, then the alternate exterior angles are congruent. Signup and view all the answers

What does the Corresponding Angles Postulate state?

If a transversal intersects parallel lines, then the corresponding angles are congruent. Signup and view all the answers

What is the statement of Theorem #1 regarding parallel lines?

If two lines are parallel to the same line, then they are parallel to each other. Signup and view all the answers

What is Theorem #2 about lines?

If two lines are perpendicular to the same line, then they are parallel to each other. Signup and view all the answers

According to Theorem #3, what can be said if a line is perpendicular to one of two lines?

It is perpendicular to the other line. Signup and view all the answers

What does the Parallel Postulate state?

Through a point not on a line, there is exactly one line parallel to the given line. Signup and view all the answers

What is stated in the Triangle Angle Sum Theorem?

The sum of the angles in a triangle is 180 degrees. Signup and view all the answers

What does the Exterior Angle Theorem claim?

The measure of the exterior angle of a triangle is the sum of the two remote interior angles. Signup and view all the answers

What can be concluded from the Third Angle Theorem?

If two angles in one triangle are congruent to two angles in another triangle, then the triangles and each angle in the triangles are congruent. Signup and view all the answers

What does the SSS Postulate state?

If three sides in one triangle are congruent to three sides in another triangle, then the two triangles are congruent. Signup and view all the answers

What is the SAS Postulate about triangle congruence?

If two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, then the two triangles are congruent. Signup and view all the answers

What does the ASA Postulate indicate?

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. Signup and view all the answers

What does the AAS Postulate state?

If two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the two triangles are congruent. Signup and view all the answers

What does the Hypotenuse-Leg Theorem claim?

If the hypotenuse and leg of one triangle and the leg of another triangle are congruent, then the triangles are congruent. Signup and view all the answers

What does CPCTC stand for?

Corresponding Parts of Congruent Triangles are Congruent. Signup and view all the answers

What does the Isosceles Triangle Theorem state?

If two sides of a triangle are congruent, then the base angles are congruent. Signup and view all the answers

What is stated in the Triangle Mid-Segment Theorem?

If a segment joins the midpoint of two sides of a triangle, then the segment is parallel to the third side. Signup and view all the answers

What can be concluded from the Perpendicular Bisector Theorem?

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Signup and view all the answers

Study Notes

Postulates

Postulate #1: One unique line can be drawn through any two points.
Postulate #2: The intersection of two lines forms exactly one point.
Postulate #3: The intersection of two planes creates a line.
Postulate #4: Only one plane can be formed through any three non-collinear points.
Ruler Postulate: Distances can be measured using a ruler between two points.
Segment Addition Postulate: In three collinear points, the sum of the lengths of the two segments equals the length of the entire segment.
Protractor Postulate: Angles can be measured from 0 to 180 degrees using a protractor.
Angle Addition Postulate: The measure of two adjacent angles that share a vertex equals the measure of the entire angle.
Linear Pair Postulate: Angles that form a linear pair are supplementary (sum to 180 degrees).

Theorems

Vertical Angle Theorem: Vertical angles are always congruent.
Theorem #1 (2.6): All right angles are congruent.
Theorem #2 (2.6): If two congruent angles are supplementary, each is a right angle.
Same Side Interior Angle Theorem: Same side interior angles formed by a transversal with parallel lines are supplementary.
Alternate Interior Angle Theorem: Alternate interior angles formed by a transversal with parallel lines are congruent.
Alternate Exterior Angle Theorem: Alternate exterior angles formed by a transversal with parallel lines are congruent.
Corresponding Angles Postulate: Corresponding angles created by a transversal across parallel lines are congruent.

Additional Theorems about Parallel Lines

Theorem #1 (3.4): Two lines parallel to the same line are parallel to each other.
Theorem #2 (3.4): Two lines perpendicular to the same line are parallel to each other.
Theorem #3 (3.4): If a line is perpendicular to one of two lines, it is also perpendicular to the other line.

Triangle Properties

Parallel Postulate: There is exactly one line parallel to a given line through a point not on that line.
Triangle Angle Sum Theorem: The sum of the interior angles in a triangle is always 180 degrees.
Exterior Angle Theorem: An exterior angle of a triangle is equal to the sum of the two remote interior angles.
Third Angle Theorem: If two angles in one triangle are congruent to two angles in another triangle, then the triangles are congruent.

Triangle Congruence Postulates

SSS Postulate: Triangles are congruent if all three sides of one are congruent to the corresponding sides of another.
SAS Postulate: Triangles are congruent if two sides and the included angle of one are congruent to the corresponding parts of another.
ASA Postulate: Triangles are congruent if two angles and the included side of one triangle are congruent to the two angles and included side of another.
AAS Postulate: Triangles are congruent if two angles and a non-included side of one triangle are congruent to the corresponding parts of another.
Hypotenuse-Leg Theorem: In right triangles, if the hypotenuse and one leg of one triangle are congruent to the corresponding parts of another right triangle, the triangles are congruent.

Congruence and Triangle Properties

CPCTC: Corresponding Parts of Congruent Triangles are Congruent.
Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the base angles are also congruent.
Triangle Midsegment Theorem: A segment that connects the midpoints of two sides of a triangle is parallel to the third side and half its length.
Perpendicular Bisector Theorem: A point on the perpendicular bisector of a segment is equidistant from the endpoints of that segment.

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Test your knowledge of essential geometry postulates and theorems with these flashcards. Each card presents a fundamental concept that is crucial for understanding geometric principles. Perfect for students looking to reinforce their understanding of geometry.