What is a radian and why is it used?

A radian is the angle subtended at the center of a circle by an arc equal in length to the radius. It is the natural unit for angles in calculus and advanced physics because it simplifies equation relations (e.g. d/dx[sinx] = cosx is only true when x is in radians).

What is the ASTC rule?

The "All Science Teachers Crazy" (or Cast) rule indicates where trig functions are positive: All are positive in Quad I, Sin in Quad II, Tan in Quad III, and Cos in Quad IV.

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Class VII Mathematics

Chapter 7: Congruence of Triangles

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Key Formulas & Equations

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Congruence SAS Theorem

\triangle ABC \cong \triangle PQR

If two sides and included angle match, triangles are congruent.

Related Formulas from Adjacent Chapters

Angle Sum Property

A + B + C = 180^\circ

[From The Triangle and its Properties] Interior angles of a triangle sum to 180 degrees.

Pythagoras Theorem

a^2 + b^2 = c^2

[From The Triangle and its Properties] Sum of squares of legs equals square of hypotenuse c in right triangle.

Profit Percentage

\%P = \frac{\text{Profit}}{\text{CP}} \times 100

[From Comparing Quantities] Profit margin relative to cost price.

Simple Interest

SI = \frac{P \times R \times T}{100}

[From Comparing Quantities] Simple interest formula.