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  2. Similarity (geometry) - Wikipedia

    en.wikipedia.org/wiki/Similarity_(geometry)

    Any two equilateral triangles are similar. Two triangles, both similar to a third triangle, are similar to each other (transitivity of similarity of triangles). Corresponding altitudes of similar triangles have the same ratio as the corresponding sides. Two right triangles are similar if the hypotenuse and one other side have lengths in the ...

  3. File:Pythagoras similar triangles simplified.svg - Wikipedia

    en.wikipedia.org/wiki/File:Pythagoras_similar...

    English: Simplified version of similar triangles proof for Pythagoras' theorem. In triangle ACB, angle ACB is the right angle. CH is a perpendicular on hypotenuse AB of triangle ACB. In triangle AHC and triangle ACB, ∠AHC=∠ACB as each is a right angle. ∠HAC=∠CAB as they are common angles at vertex A.

  4. AA postulate - Wikipedia

    en.wikipedia.org/wiki/AA_postulate

    In Euclidean geometry, the AA postulate states that two triangles are similar if they have two corresponding angles congruent. The AA postulate follows from the fact that the sum of the interior angles of a triangle is always equal to 180°. By knowing two angles, such as 32° and 64° degrees, we know that the next angle is 84°, because 180 ...

  5. File:Pythagoras by similar triangles.svg - Wikipedia

    en.wikipedia.org/wiki/File:Pythagoras_by_similar...

    Area of triangle C = sum of areas of A and B. All three right triangles are similar, so all three areas are proportional to the side bordering the centre triangle. Hence, α(a2 + b2) = α c2, or dividing by α, we have Pythagoras' theorem.

  6. Cognate linkage - Wikipedia

    en.wikipedia.org/wiki/Cognate_linkage

    From original triangle, ΔA 1 DB 1: Sketch Cayley diagram. Using parallelograms, find A 2 and B 3 O A A 1 DA 2 and O B B 1 DB 3. Using similar triangles, find C 2 and C 3 ΔA 2 C 2 D and ΔDC 3 B 3. Using a parallelogram, find O C O C C 2 DC 3. Check similar triangles ΔO A O C O B. Separate left and right cognate. Put dimensions on Cayley diagram.

  7. Assisted living options for wheelchair users - AOL

    www.aol.com/assisted-living-options-wheelchair...

    Benefits of Assisted Living for Wheelchair Users. Compared to independent living, assisted living can provide a wider breadth of support. These services provide a safe and comfortable atmosphere ...

  8. Where home prices are forecast to increase most in the coming ...

    www.aol.com/finance/where-home-prices-forecast...

    Home value increase between August 2023 and August 2024: 10.9%. 90275: Rancho Palos Verdes, CA. Projected dollar increase in home prices: $22,146. Projected percentage increase in home prices: 1.2%.

  9. Napoleon points - Wikipedia

    en.wikipedia.org/wiki/Napoleon_points

    The three triangles XBC, YCA, ZAB erected over the sides of the triangle ABC need not be isosceles for the three lines AX, BY, CZ to be concurrent. [5] If similar triangles XBC, AYC, ABZ are constructed outwardly on the sides of any triangle ABC then the lines AX, BY, CZ are concurrent.

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