G.31.b

Investigate, prove, and apply theorems about triangles, including but not limited to: the sum of the measures of the interior angles of a triangle is 180˚; the base angles of isosceles triangles are congruent; the segment joining the midpoints of two sides of a triangle is parallel to the third side and half the length; a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem using triangle similarity.

Khan Academy Resources

Intro to inverse trig functionsSolving for a side in right triangles with trigonometryAngles of elevation and depressionTrigonometric ratios in right trianglesRight triangle trigonometry reviewSpecial right triangles reviewHypotenuse, opposite, and adjacentSolve for a side in right trianglesSpecial right trianglesTrigonometric ratios in right trianglesProve theorems using similarityPythagorean theorem challengeProve triangle propertiesSolve for an angle in right trianglesRight triangle trigonometry word problemsSolving for a side in right triangles with trigonometryTrigonometric ratios in right trianglesProof of the quadratic formulaProofs concerning isosceles trianglesProofs concerning equilateral trianglesSpecial right triangles proof (part 2)Special right triangles proof (part 1)30-60-90 triangle example problemIntro to angle bisector theoremExploring medial trianglesArea of a regular hexagonProving triangle medians intersect at a pointMulti-step word problem with Pythagorean theoremProof: Parallel lines divide triangle sides proportionallyRight triangle word problemUsing right triangle ratios to approximate angle measure

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