【Haichuan Teahouse】Brain-teasing Series: Do you have any good ideas?
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As shown in the figure, ∠CED = 90 degrees, DE = 8, CE = 6. Find the area of △ADG. abcd and defg are squares; some people thought of cutting, complementing, and transformation. Do you have any good methods to share?
The height of this shadow on DG is also 6
S=1/2absinα, sin∠ADG=sin∠CDE
Just use the formula for triangles to calculate it; agree with the person in post 4
As shown, the extended line segment GD intersects line segment AB at point H; it can be proven that triangles CDE and AHD are similar triangles； By using similar triangles, it can be determined that AH is equal to 7.5 ； HD is equal to 12.5; using the formula for the area of a triangle, it can be determined that AK is equal to 6. Therefore, the hidden area = 6*8/2 = 24
Triangle 1 and Triangle 2 are congruent: victory:
You’re looking at it wrong; 1 and 2 are not congruent, they are similar. CD=AD, but CD is the hypotenuse of triangle 2, while AD is a leg of triangle 1
This post was last edited by Yang Qing on 2022-7-14 at 11:37. What I mean is that in your diagram, AKD is entirely equal to DCE (rotate triangle DCE 90 degrees counterclockwise with point D as the pivot)
Two congruent triangles. Pythagorean hypotenuse for 6/8/10, no calculator needed
:) If you mark the length of each side for both triangles, you’ll be able to tell whether they are similar or congruent. You are on the wrong track:D