![]() ![]() Marla walks straight from the parking lot to the ocean. Relating to the Real WorldRecreationAt the parking lot of a State Park, the 300-m path to the snack bar and the 400-m path to the boat rental shop meet at a right angle. Solve for the other missing lengths given only two measurements.a = 4, b = 6a = 8, c = 10a = 5, m = 7a = 9, n = 6a = 12, h = 9b = 6, c = 15b = 8, m = 9b = 4, n = 3b = 11, h = 8c = 18, m = 12c = 15, n = 8c = 20, h = 6m = 12, n = 8m = 9, h = 12n = 10, h = 12 Theorem: If two triangles have one angle of a triangle equal to one angle of the other, and the sides about those equal angles are proportional, then the. Geometric Mean-Altitude Theorem 2The altitude to the hypotenuse to a right triangle intersects it to that the length of each leg us the geometric mean of the length of its adjacent segment of the hypotenuse and the length of the entire hypotenuseBACB=CBBD ABCA=CAAD □□=□□×□□ □□=□□×□□ Geometric Mean-Altitude Theorem 1The length of the altitude to the hypotenuse is the geometric mean of the lengths of the segments of the hypotenuse.CABD□□□□=□□□□ □□=□□×□□ Right Triangle and Special Right Triangle. SAS, SSS, AA Similarity Theorems along with the. Right Triangle Similarity TheoremThe altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other.CABDABC ~ ACD ~ CBD There are several ways to prove certain triangles are similar. Parts of a right triangle incorporated with the altitudeCLeg adjacent to DBLeg adjacent to ADABDSegments of the hypotenuse AD and DB In this case, you can prove that two triangles are similar if two of their corresponding angles are equal. We can see that the three triangles are similar to each other. The AA similarity theorem is named after angle angle. We orient the three triangles to see the them clearer.BigSmallMedium There are a three triangles in the figure below. This divides the original triangle into two smaller right triangle: ΔBDC This divides the original triangle into two smaller right triangle: ΔDCA ![]() This divides the original triangle into two smaller right triangle: ![]()
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