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

Question

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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

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

Answer

Step-by-step solution

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

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.

The legs of the trapezoid are the hypotenuses of these right triangles.

The left overhanging segment has length $4 - x$ .

Set the overhanging segments equal

Add $x$ to both sides

Divide both sides by 2

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

Answer

Step-by-step solution

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

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.

The legs of the trapezoid are the hypotenuses of these right triangles.

The left overhanging segment has length 4−x4 - x4−x.

Set the overhanging segments equal

Add xxx to both sides

Divide both sides by 2

Try one yourself

Still stuck on this one?

More Mathematics Questions

The left overhanging segment has length $4 - x$ .

Add $x$ to both sides