Démontre que les deux triangles bleus à l'intérieur de la figure sont isométriques.

Mathematics
Démontre que les deux triangles bleus à l'intérieur de la figure sont isométriques.

ScanSolve AI Answer

Answer

2

Step 1: In an isosceles trapezoid, the non-parallel sides (legs) are equal in length.

Step 2: Drop perpendiculars from the endpoints of the shorter top base to the longer bottom base, forming two right triangles on either end and a rectangle in the middle.

Step 3: The legs of the trapezoid are the hypotenuses of these right triangles. For the legs to be equal, the right triangles must have equal base lengths (the overhanging segments).

Step 4: The left overhanging segment has length 4x4 - x.
The right overhanging segment has length xx.

Step 5: Set the overhanging segments equal:
4x=x4 - x = x

Step 6: Add xx to both sides:
4x+x=x+x4 - x + x = x + x
4=2x4 = 2x

Step 7: Divide both sides by 22:
x=42x = \frac{4}{2}
x=2x = 2

2\boxed{2}

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Quick Answer

In an isosceles trapezoid, the non-parallel sides (legs) are equal in length. Step 2: Drop perpendiculars from the endpoints of the shorter top base to the longer bottom base, forming two right triangles on either end and a rectangle in the middle.

Démontre que les deux triangles bleus à l'intérieur de la figure sont isométriques.
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
Step 1: In an isosceles trapezoid, the non-parallel sides (legs) are equal in length. Step 2: Drop perpendiculars from the endpoints of the shorter top base to the longer bottom base, forming two right triangles on either end and a rectangle in the middle. Step 3: The legs of the trapezoid are the hypotenuses of these right triangles. For the legs to be equal, the right triangles must have equal base lengths (the overhanging segments). Step 4: The left overhanging segment has length 4 - x. The right overhanging segment has length x. Step 5: Set the overhanging segments equal: 4 - x = x Step 6: Add x to both sides: 4 - x + x = x + x 4 = 2x Step 7: Divide both sides by 2: x = (4)/(2) x = 2 2