DSE數學--方程式/定理(theorem)列表 Trigonometry

DSE數學--方程式/定理(theorem)列表 Trigonometry

1. General theorem

• Pyth. thm. (Pythagorean Theorem)

The sum of the squares of the legs of a right triangle equals the square of its hypotenuse

• Converse of Pyth. thm

IF the sum of the square of the length of two sides is equal to the square of the length of remaining side, the triangle is a right-angled triangle in which a right angled is located between the "two sides"

• ∠ sum of ∆

 The sum of interior angles of triangle is equal to 180°

• ext. ∠ of ∆

An exterior angle of a triangle is equal to the sum of two non-adjacent interior angles of the triangle.

• base ∠s, isos. ∆

The base angles of an isosceles triangle are equal.

• sides opp. eq.∠s

When two of the interior angles of a triangle are equal, the sides opposite to those interior angles are equal(i.e. form a isosceles triangle)

• greater ∠, greater side
• greater side, greater ∠

2. Similar/congruent triangle 

• Prove similar triangle: AA / three sides proportional / ratio of 2 sides, included angle 

Above are three ways to prove whether a pair of triangle is similar. Click to know more.

• Prove congruent triangle: RHS / SSS / SAS / ASA / AAS

Above are five ways to prove whether a pair of triangle is congruent. Click to know more.

• Properties of similar triangle: corr. sides, ~∆s /corr. ∠s, ~∆s 

Above are two properties of similar triangles. Click to know more.

• Properties of congruent triangle: corr. sides, ≊∆s /corr. ∠s, ≊∆s 

Above are two properties of congruent triangles. Click to know more.