Geometry 101: Parallel & Triangle Reasons | 聽歌温數學 | Reasons逐個數 | Jacky Sir

Trace out a single plane, draw a straight line, Where adjacent angles on a straight line perfectly align. When two straight lines intersect, X marks the spot— Vertically opposite angles are equal, truth on the dot! When lines meet at a point, the rotation’s complete, Angles at a point make 360 degrees meet. [Chorus] Behold a pair of parallel lines, AB parallel to CD, Unlocking the geometric patterns that we see. Corresponding angles equal—AB parallel to CD, Alternate angles equal—AB parallel to CD, Interior angles sum to 180 degrees—AB parallel to CD, The ultimate reasons written down for our proof decree! Now flip the perspective, reverse the entire design: To prove two lines parallel, we trace the converse line. To show corresponding angles equal in their space, Or alternate angles equal in the exact same place, Or interior angles supplementary—add up the score, And those lines are parallel forevermore! [Chorus] Step inside a triangle, a three-sided domain, The angle sum of a triangle is a constant on this plane. Look outside at the exterior angle of a triangle in view: It equals the sum of the opposite interior two! If two sides are equal, it’s an isosceles triangle defined, Where the base angles of an isosceles triangle are aligned. Flip the logic: if two angles are equal, then two opposite sides equal in length, By sides opposite equal angles, proving its mathematical strength. When three sides are equal, it’s an equilateral triangle we trace, Where all angles equal 60 degrees in every single case. This flawless balance is the property of an equilateral triangle clear, But shift to a square corner when a right-angled triangle is near. We use the Pythagorean Theorem to crack the unknown side, While sine theta, cosine theta, and tangent theta act as our guide. With these trig ratios mastered, we confidently take control, To find the unknowns—the final victory of our soul! To find the unknowns... AB parallel to CD. Angles at a point, 360 degrees, we're free!