Geometry

What is a 'Point' in geometry?

A position in space with no breadth or width.

What is a 'Line' in geometry?

All points that continue in both directions that connect through two points.

What is a 'Plane' in geometry?

All points that share a flat 2D surface.

What does it mean for points to be 'Collinear'?

They are all points that share a line.

What does it mean for points to be 'Coplanar'?

They are all points that share a plane.

What is a 'Line Segment'?

A portion of a line between two endpoints, including the endpoints.

What is a 'Midpoint'?

The point that divides a line segment into two equal parts.

What does it mean to 'Bisect' a line segment?

To cut it into two equal pieces, which passes through the midpoint.

What is a 'Ray' in geometry?

All points that continue endlessly from a starting point in one direction.

What are 'Opposite Rays'?

Two rays that share a midpoint and form a line.

What is an 'Angle' in geometry?

Two rays with a common endpoint.

What does 'Equality' mean in a geometric context?

Having an equal measure.

What does 'Congruency' mean in a geometric context?

Having the same shape and size.

An angle that measures exactly 90° is called a _.

Right angle

An angle that measures less than 90° is called an _.

Acute angle

An angle that measures more than 90° is called an _.

Obtuse angle

What are 'Complementary angles'?

Two angles that add up to 90°.

What are 'Supplementary angles'?

Two angles that add up to 180°.

What is a 'Linear pair' of angles?

Adjacent, supplementary angles that intersect and equal 180°.

What are 'Vertical angles'?

Two angles that intersect and mirror each other, sharing a vertex but not sides.

What defines 'Parallel lines'?

Lines that are coplanar and never intersect.

What are 'Perpendicular lines'?

Lines that intersect to form right angles.

What are 'Skew lines'?

Lines that are not parallel but never intersect (they are not on the same plane).

What is a 'Polygon'?

A closed figure whose straight sides are not intersecting.

A polygon that is both equilateral and equiangular is known as a _.

Regular polygon

What is an 'Equilateral polygon'?

A polygon where all sides are equal.

What is an 'Equiangular polygon'?

A polygon where all angles are equal.

What is a 'Scalene triangle'?

A triangle with all sides of different lengths.

What is an 'Equilateral triangle'?

A triangle where all sides have the same length.

What is an 'Isosceles triangle'?

A triangle with at least two congruent sides.

What is a 'Parallelogram'?

A quadrilateral with two sets of parallel sides.

What is a 'Trapezoid'?

A quadrilateral with exactly one set of parallel sides.

What is an 'Isosceles Trapezoid'?

A trapezoid with one set of opposite sides congruent.

What is a 'Kite'?

A quadrilateral with two sets of consecutive congruent sides.

A 'Rhombus' is defined as an equilateral _.

Parallelogram

A 'Rectangle' is defined as an equiangular quadrilateral with _.

Two pairs of congruent opposite sides.

What is a 'Square'?

A regular parallelogram (equilateral and equiangular).

What is a 'Rigid' transformation?

A transformation that results in the same shape and size.

What is a 'Non-Rigid' transformation?

A transformation that results in the same shape but a different size.

A shift left/right or up/down is a transformation known as a _.

Translation

A 'Reflection' is a transformation that creates a _ image.

Mirror

A 'Rotation' is a transformation that results in a change in _.

Position

A 'Dilation' is a transformation that results in a change in _.

Size (enlargement/reduction)

What does a 'Translation vector' describe?

The direction and magnitude of a translation.

What is the 'Line of reflection'?

The line that a shape is reflected over.

How does a reflection affect a shape's orientation?

The shape and size are congruent, but the orientation is opposite.

How does a translation affect a shape's size and orientation?

The shape, size, and orientation are all congruent (the same).

How does a rotation affect a shape's size and orientation?

The shape and size are congruent, but the orientation is different.

What is the definition of a 'Circle'?

All points equidistant from a center point.

What is the 'Radius' of a circle?

The distance from the center to any point on the circle.

What is a 'Chord' of a circle?

A line segment with both endpoints on the circle.

What is the 'Diameter' of a circle?

A chord that passes through the center of the circle.

What is a 'Tangent' to a circle?

A line or segment with exactly one point on the circle, and that point is perpendicular to the radius.

What are 'Concentric' circles?

Circles that have the same center but different radii.

What does it mean for a shape to be 'Circumscribed'?

It is a shape that surrounds another shape.

What does it mean for a shape to be 'Inscribed'?

It is a shape inside another shape.

What is 'Inductive reasoning'?

Finding a pattern and arriving at a conjecture.

What is 'Deductive reasoning'?

Starting with a premise accepted as true and using applied truths that follow logically to arrive at a proven conclusion.

The _ states that if $a=b$, then $a+c = b+c$.

Addition Property of Equality

The _ states that if $a=b$, then $a-c = b-c$.

Subtraction Property of Equality

The _ states that if $a=b$, then $ac = bc$.

Multiplication Property of Equality

The _ states that if $a=b$, then $a/c = b/c$.

Division Property of Equality

What is the Substitution Property of Equality?

If $a=b$, then $a$ can be replaced with $b$.

The _ states that for any real number $a$, $a=a$.

Reflexive Property of Equality

The _ states that if $a=b$, then $b=a$.

Symmetrical Property of Equality

The _ states that if $a=b$ and $b=c$, then $a=c$.

Transitive Property of Equality

What is the Linear Pair Conjecture?

If two angles form a linear pair, then their measures sum to 180°.

What is the Vertical Angles Conjecture?

If two angles are vertical angles, then they are congruent.

What is the Corresponding Angles Conjecture?

If two parallel lines are cut by a transversal, then corresponding angles are congruent.

What is the Alternate Interior Angles Conjecture?

If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

What is the Alternate Exterior Angles Conjecture?

If two parallel lines are cut by a transversal, then alternate exterior angles are congruent.

What is the Converse of Parallel Lines conjecture?

If two lines are cut by a transversal to form pairs of congruent corresponding, alternate interior, or alternate exterior angles, then the lines are parallel.

What is Modus Ponens?

If a conditional statement ($P \rightarrow Q$) is true, and its antecedent ($P$) is true, then the consequent ($Q$) must also be true.

What is Modus Tollens?

If a conditional statement ($P \rightarrow Q$) is true, and the consequent ($Q$) is false (not $Q$), then the antecedent ($P$) must also be false (not $P$).

The _ is a rule that connects two true conditional statements to form a new, true conditional statement.

Law of Syllogism

What is the 'Converse' of the conditional statement 'if P then Q'?

If Q then P.

What is the 'Inverse' of the conditional statement 'if P then Q'?

If not P then not Q.

What is the 'Contrapositive' of the conditional statement 'if P then Q'?

If not Q then not P.

A _ combines a conditional statement and its converse when both are true, using the phrase 'if and only if'.

Bi-conditional statement

What is the Triangle Sum Conjecture?

The sum of the measures of the angles in every triangle is 180°.

What is the Isosceles Triangle Conjecture?

If a triangle is isosceles, then it has two congruent sides and two congruent base angles.

What does CPCTC stand for?

Corresponding Parts of Congruent Triangles are Congruent.

Which triangle congruency postulate uses two pairs of congruent sides and the congruent angle between them?

SAS (Side-Angle-Side)

Which triangle congruency postulate uses three pairs of congruent sides?

SSS (Side-Side-Side)

Which triangle congruency postulate uses two pairs of congruent angles and the congruent side between them?

ASA (Angle-Side-Angle)

Does the AAA (Angle-Angle-Angle) condition prove that two triangles are congruent?

No, it only proves similarity, not congruence.

What is the formula for the sum of the interior angles of a polygon with 'n' sides?

$180(n-2)$

The sum of the exterior angles of any convex polygon always equals _.

360°

What is the Kite Diagonals Conjecture?

The diagonals of a kite are perpendicular.

In a kite, the diagonal connecting the vertex angles is the _ of the other diagonal.

bisector

What is the Trapezoid Consecutive Angles Conjecture?

The consecutive angles between the bases of a trapezoid are supplementary.

What is the Isosceles Trapezoid Diagonals Conjecture?

The diagonals of an isosceles trapezoid are congruent.

The _ of a triangle is parallel to the third side and is half the length of the third side.

midsegment

The _ of a trapezoid is parallel to the bases and is equal in length to the average of the bases.

midsegment

What is the slope-intercept form of a linear equation?

$y = mx + b$

What is the point-slope form of a linear equation?

$y - y1 = m(x - x1)$

What is the standard form of a linear equation?

$Ax + By = C$

What is the formula to calculate the slope ($m$) between two points $(x1, y1)$ and $(x2, y2)$?

$m = \frac{y2 - y1}{x2 - x1}$

What is the coordinate rule for a 90° counter-clockwise rotation about the origin?

$T(x,y) \rightarrow (-y,x)$

What is the coordinate rule for a 180° rotation about the origin?

$T(x,y) \rightarrow (-x,-y)$