【Haichuan Teahouse】Brain-teasing Geometry: Find the Length of the Red Side
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In the triangle, the red side intersects the segment of length 4 at the midpoint of the base. The lengths of the other two sides of the triangle are shown in the figure; find the length of the red side.
That’s correct, but using a square root gives more precision... I tried to draw a diagram (which also represents the solution), and the value indicated to one decimal place is 14.4.
How to prove that ∠BCO = 90 degrees? It can be shown that when ∠BCO = 90 degrees, AB = 2√(62 + 42) = 14.4222
For example, using the 3rd floor as a auxiliary line to form a triangle, 8 squared plus 6 squared equals 10 squared, which satisfies the conditions of a right triangle……
This post was last edited by Wang Genrong on 2021-12-11 at 14:53. By drawing a line AD parallel to BC and extending CO to meet D, can it be determined that OD=4? AD is parallel to BC, AO = BO; △AOD and △BCO are congruent triangles, with DO = OC = 4, satisfying the conditions of the Pythagorean theorem.
Taking CO as a extension and setting its value to 4, then proving congruence using the sequence \"side, angle, side\", we find that AD equals 6; this yields a triangle with side lengths of 6, 8, and 10, proving that it is a right triangle.
Well, your revised proof also holds! The key is to draw auxiliary lines……
It proves that OD=4; it cannot take the value 4.
Using geometric methods to find that OD is equal to 4 – I’m not sure if this is allowed in junior high school math……
Proving congruence by drawing parallel lines follows the \"angle, side, angle\" method: victory: