Mathematics 9 Reviewer: Triangle Theorems, Geometric Constructions, and Quadratic Transformations

Vocabulary flashcards covering triangle theorems, geometric constructions, two-column proofs, and quadratic transformations from Mathematics 9 Term 2 Weeks 4 to 6.

Hypotenuse-Leg (HL) Theorem

A congruence theorem stating that if two right triangles have congruent hypotenuses and one pair of corresponding legs congruent, then the triangles are congruent.

Isosceles Triangle Theorem

A theorem stating that if a triangle is isosceles (two sides are congruent), then its base angles are congruent.

Perpendicular Bisector of a Segment

A line perpendicular to a segment that divides it into two equal parts; any point on it is equidistant from the endpoints of the segment, and any point equidistant from the endpoints lies on it.

Triangle Midline Theorem

A theorem stating that the segment joining the midpoints of two sides of a triangle is parallel to the third side and its length is half the length of the third side ($\text{DE} \parallel \text{BC}$ and $\text{DE} = \frac{1}{2}\text{BC}$).

Angle Bisector

A ray that divides an angle into two congruent angles, such that if ray $OC$ bisects $\angle AOB$, then $\angle AOC = \angle COB$.

Triangle Inequality

The geometric principle stating that for any triangle to be constructed from three side lengths, the sum of the lengths of any two sides must be strictly greater than the length of the third side.

CPCTC

An abbreviation for "Corresponding Parts of Congruent Triangles are Congruent," used as a reason in proofs after two triangles are proven congruent to establish that corresponding sides or angles are equal.

Parent Quadratic Function

The basic quadratic function $y = x^2$, whose graph is a U-shaped parabola opening upward with its vertex at $(0, 0)$ and its axis of symmetry along the y-axis ($x = 0$).

Axis of Symmetry (Quadratic)

The vertical line about which a parabola is symmetric; for the parent function $y = x^2$, it is the y-axis, defined by the equation $x = 0$.

Vertex of a Parabola

The lowest point of an upward-opening parabola or the highest point of a downward-opening parabola; located at $(0, 0)$ for the basic parent function $y = x^2$.

Vertical Shift (Quadratic)

A transformation of the form $y = x^2 + k$ that moves the graph of $y = x^2$ upward by $|k|$ units when $k > 0$ and downward by $|k|$ units when $k < 0$.

Horizontal Shift (Quadratic)

A transformation of the form $y = (x - h)^2$ that moves the graph of $y = x^2$ to the right by $|h|$ units when $h > 0$ and to the left by $|h|$ units when $h < 0$.

Reflection over the x-axis (Quadratic)

A transformation represented by the equation $y = -x^2$, causing the parabola to open downward with its vertex remaining at $(0, 0)$.