Mathematics | MAT41 Grade 09 | Advanced 7.5 Practice Flashcards

This set of flashcards covers key vocabulary and geometric theorems from Grade 09 Math Advanced 7.5 lecture notes, including 2D representations, logic, coordinate geometry, transformations, and triangle congruence.

Orthographic drawing

A two-dimensional representation of a three-dimensional figure that typically includes the top, front, and side views.

Surface Area of a Triangular Prism

Calculated by the formula $S = Pl + 2B$, where $P$ is the perimeter of the base, $l$ is the length, and $B$ is the area of the base.

Conjecture

A statement that describes a pattern in a sequence or relationship, often used to predict the next term or value.

Arithmetic sequence

A sequence of numbers where the difference between consecutive terms is constant, known as the common difference.

Counterexample

An example that demonstrates a conjecture is false by showing a specific instance where the statement does not hold true.

Supplementary angles

Two angles whose measures have a sum of $180^\circ$.

Complementary angles

Two angles whose measures have a sum of $90^\circ$.

Linear pair

A pair of adjacent angles whose non-common sides are opposite rays, making them supplementary.

Conjunction ($p \wedge q$)

A compound statement formed by joining two statements with the word 'and'; it is only true if both individual statements are true.

Disjunction ($p \vee q$)

A compound statement formed by joining two statements with the word 'or'; it is true if at least one of the individual statements is true.

Conditional statement

A statement that can be written in if-then form, represented as $p \rightarrow q$.

Hypothesis

The phrase immediately following the word 'if' in a conditional statement.

Conclusion

The phrase immediately following the word 'then' in a conditional statement.

Converse

Formed by exchanging the hypothesis and the conclusion of a conditional statement.

Inverse

Formed by negating both the hypothesis and the conclusion of a conditional statement.

Contrapositive

Formed by negating both the hypothesis and the conclusion of the converse of a conditional statement.

Supplement Theorem

States that if two angles form a linear pair, then they are supplementary angles.

Complement Theorem

States that if the non-common sides of two adjacent angles form a right angle, then the angles are complementary.

Alternate interior angles

Inner angles on opposite sides of the transversal that do not share a vertex.

Alternate exterior angles

Outer angles on opposite sides of the transversal that do not share a vertex.

Consecutive interior angles

Inner angles on the same side of the transversal; they are supplementary when the lines are parallel.

Corresponding angles

Angles in the same relative position at each intersection where a straight line crosses two others.

Vertical Angles Theorem

States that vertical angles (opposite angles formed by the intersection of two lines) are congruent.

Distance Formula

$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

Reflection in the line $y = x$

A transformation that maps the point $(x, y)$ to the image $(y, x)$.

Translation vector

A vector $\langle a, b \rangle$ that describes the horizontal and vertical shift of a figure in the coordinate plane.

$180^\circ$ counterclockwise rotation

A transformation about the origin that maps $(x, y)$ to $(-x, -y)$.

$90^\circ$ counterclockwise rotation

A transformation about the origin that maps $(x, y)$ to $(-y, x)$.

$270^\circ$ counterclockwise rotation

A transformation about the origin that maps $(x, y)$ to $(y, -x)$.

Line symmetry

A property where a figure can be folded along a line so that the two halves match exactly.

Rotational symmetry

A property where a figure can be rotated about its center point by an angle less than $360^\circ$ and still look the same as the original figure.

Magnitude of symmetry

The smallest angle through which a figure can be rotated to map onto itself, calculated as $360^\circ / \text{order}$.

Triangle Angle-Sum Theorem

The sum of the measures of the interior angles of a triangle is $180^\circ$.

Exterior Angle Theorem

States that the measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

CPCTC

An abbreviation for "Corresponding Parts of Congruent Triangles are Congruent."

SSS Congruence Postulate

States that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

SAS Congruence Postulate

States that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

ASA Congruence Postulate

States that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

AAS Congruence Theorem

States that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Third Angle Theorem

If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are also congruent.