IM2 review for fall finals_2023

Front

What does it mean for triangles to be similar?

Back

Triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Front

How do you find the value of x in a triangle?

Back

Use the properties of angles in triangles, such as the sum of angles being 180 degrees, or apply trigonometric ratios if applicable.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.

Front

How do you factor a quadratic expression like x² - 15x + 36?

Back

To factor, find two numbers that multiply to 36 (the constant term) and add to -15 (the coefficient of x). The factors are (x - 12)(x - 3).

Front

What is the AAS postulate in triangle congruence?

Back

The AAS (Angle-Angle-Side) postulate states that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What is the SAS postulate in triangle congruence?

Back

The SAS (Side-Angle-Side) postulate states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What is the ASA postulate in triangle congruence?

Back

The ASA (Angle-Side-Angle) postulate states that if two angles and the included side of one triangle are equal to two angles and the corresponding included side of another triangle, then the triangles are congruent.

Front

What is the difference between a linear equation and a quadratic equation?

Back

A linear equation has the form y = mx + b, representing a straight line, while a quadratic equation has the form y = ax² + bx + c, representing a parabola.

Front

How do you determine if two triangles are congruent?

Back

Use congruence postulates such as SSS, SAS, ASA, AAS, or HL (Hypotenuse-Leg for right triangles) to determine if two triangles are congruent.

Front

What is the significance of the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola, making it easy to identify the vertex and the direction of the parabola.