# Geometry Terms

## 50 terms · Vocabulary, Theorems, and Postulates for Geometry Honors

### Inductive Reasoning

Inductive Reasoning is arriving to a conclusion based on a set of observations. It is looking at patterns and making predictions based on these patterns.

### Conjecture

A conjecture is an unproven statement that is based on observations

### Conditional Statement

A conditional statement is a logical statement with a hypothesis and a conclusion

### If/Then Form

: If/Then form is a way of writing conditional statements. It follows the pattern If p, then q (p is hypothesis, q is conclusion)

### Counterexample

A counterexample is a specific case for which the conjecture is false. You can find a conjecture false by simply finding one counterexample.

### Converse

If q, then p (if conclusion, then hypothesis)

### Inverse

If not p, then not q (if not hypothesis, then not conclusion)

### Contrapositive

If not q, then not p (if not conclusion, then not hypothesis)

### Biconditional Statement

When a conditional statement and its converse are both true, you can write them as a single biconditional statement (if and only if...)

### Perpendicular Lines

If 2 lines intersect to form a right angle, they are perpendicular

• Converse: If 2 lines are perpendicular, they intersect to form a right angle
• Inverse: If 2 lines don't intersect to form a right angle, then they aren't perpendicular
• Contrapositive: If 2 lines aren't perpendicular, then they don't intersect to form a right angle
• Biconditional: 2 lines intersect to form a right angle if and only if they are perpendicular

### Deductive Reasoning

Uses facts, rules, definitions, or properties to arrive at a conclusion

### Law of Detachment

If hypothesis, then conclusion is a true conditional statement, and the hypothesis is true (it occurs), then the conclusion is true.

• If (insert students name here) gets an A on his test, he will be happy
• He gets an a on his test, therefore, he will be happy

### Law of Syllogism

If p then q and q then r are true conditional statements, the p then r is true.

• If (insert student here) doesn't fail the test, he will pass his math class
• If he passes his math class, he will graduate
• Therefore, if he doesn't fail the test, he will graduate

If B is between A and C, then AB+BC = AC. If AB+BC=AC, then B is somewhere in between A and C.

If P is in the interior of ∠RST, then m∠RST = m∠RSP + m∠PST

### Through any two points there exists exactly ______

One line. (Postulate 5: Through any two points there exists exactly one line)

### A line contains at least _______

Two points. (Postulate 6: A line contains at least two points)

### If two lines intersect, their intersection is exactly ______

One point. (Postulate 7: If two lines intersect, then their intersection is exactly one point)

### Through any three non collinear points there exists exactly one _____

Plane. (Postulate 8: Through any three noncollinear points there exists exactly one plane)

### A plane contains at least ______

Three non-collinear points. (Postulate 9: A plane contains at least three noncollinear points)

### If two points lie on a plane, then the line containing them lies in the ______

Same plane. (Postulate 10: : If two points lie in a plane, then the line containing them lies in the plane)

### Linear Pair Postulate

If two angles form a linear pair, then they are supplementary

### Properties of Segment Congruence

Segment congruence is reflexive, symmetric, and transitive

• Reflexive: For any segment AB, AB≅AB
• Symmetric: If AB≅CD, then CD≅AB
• Transitive: If AB≅CD and CD≅EF, then AB≅EF

### Properties of Angle Congruence

Angle congruence is reflexive, symmetric, and transitive

• Reflexive: For any angle A, ∠A≅∠A
• Symmetric: If ∠A≅∠B, then ∠B≅∠A
• Transitive: If ∠A≅∠B and ∠B≅∠C, then ∠A≅∠C

### Right Angles Congruence Theorem

All right angles are congruent

### Congruent Supplements Theorem

If two angles are supplementary to the same angle (or to congruent angles), then the two angles are congruent

### Congruent Complements Theorem

If two angles are complementary to the same angle (or to congruent angles), then the two angles are congruent

### Vertical Angles Congruence Theorem

Vertical angles are congruent

### Congruent Segments

Line segments that have the same length

### Congruent Angles

Angles that have the same measure

### Midpoint

A point that divides the segment into two congruent segments

### Right Angle

An angle whose measure is equal to 90 degrees`

### Acute Angle

An angle who's measure is less than 90 degrees

### Obtuse Angle

An angle whose measure is greater than 90 degrees

### Straight Angle

An angle whose measure is 180 degrees

### Collinear Points

Points that are on the same line

### Coplanar Points

Points that are on the same plane

### Angle Bisector

A ray that cuts in half an angle into two angles that are congruent

### Linear Pair

Two adjacent angles whose noncommon sides are opposite rays

### Vertical Angles

Two angles that their sides form two pairs of opposite rays

### Supplementary Angles

Two angles whose measures have a sum of 180 degrees

### Complementary Angles

Two angles whose measures have a sum of 90 degrees

Two angles that share a common vertex, side, or ray

### Perpendicular Lines

Two lines that intersect to form a right angle

### If two lines intersect to form a linear pair of congruent angles, then _________

If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular

### If two lines are perpendicular, then _________________

If two lines are perpendicular, then they intersect to form four right angles

### If two sides of two adjacent acute angles are perpendicular, then ________

If two sides of two adjacent acute angles are perpendicular, then the angles are complementary

### If a transversal is perpendicular to one of two parallel lines, then ________

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other

### In a plane, if two lines are perpendicular to the same line, then _______

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other

### Distance from a point to a line

The length of the perpendicular segment form the point to the line (shortest distance b/w point and line)