Angles and triangles
Any spelling of the right answer counts: 0.5 or 1/2, pi/2 or π/2, sine or cosine for the same graph.
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About Angles and triangles
Geometry starts with angles. Angles that make a straight line add to 180°, angles that make a corner add to 90°, and when two lines cross, the angles across from each other are equal. Parallel lines cut by a third line repeat the same angles over and over.
Triangles bring the famous facts: the three angles add to 180°, and in a right triangle the sides obey a² + b² = c². The 45-45-90 and 30-60-90 triangles are worth memorizing, similar triangles have sides in proportion, and SOH-CAH-TOA turns an angle into a ratio of sides.
Keep in mind
- Complementary angles add to 90°, supplementary angles add to 180°.
- Vertical angles are equal. On parallel lines, corresponding and alternate angles are equal; same-side interior angles add to 180°.
- The angles of a triangle add to 180°. An exterior angle equals the two remote interior angles added.
- Pythagoras: a² + b² = c², with c the hypotenuse.
- 45-45-90: legs equal, hypotenuse = leg × √2. 30-60-90: sides 1 : √3 : 2.
- SOH-CAH-TOA: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.
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