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 6: The Triangle and its Properties

Standard NCERT & CBSE aligned study curriculum. Master concepts, track accuracy, revise weak areas, and challenge yourself with 9 customized practice modes.

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Key Formulas & Equations

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Angle Sum Property

A + B + C = 180^\circ

Interior angles of a triangle sum to 180 degrees.

Pythagoras Theorem

a^2 + b^2 = c^2

Sum of squares of legs equals square of hypotenuse c in right triangle.

Related Formulas from Adjacent Chapters

Supplementary Angles

\theta_1 + \theta_2 = 180^\circ

[From Lines and Angles] Sum of supplementary angles is a straight angle.

Complementary Angles

\theta_1 + \theta_2 = 90^\circ

[From Lines and Angles] Sum of complementary angles is a right angle.

Congruence SAS Theorem

\triangle ABC \cong \triangle PQR

[From Congruence of Triangles] If two sides and included angle match, triangles are congruent.