Description

est-ce que deux triangles rectangles sont semblables ?

**Answer:**

Yes, two right-angled triangles are similar if they meet certain conditions. Here’s a concise explanation:

1. **Equal Angles:** For two right-angled triangles to be similar, they must have equal corresponding angles. Since both triangles are right-angled (90 degrees), if another acute angle is equal, the third angle will automatically be equal as well (since the sum of angles in a triangle is 180 degrees). Therefore, if one acute angle is equal, the triangles are similar.

2. **Proportional Sides:** Alternatively, if the corresponding sides of the two triangles are in proportion, the triangles are similar. This means that the ratio of the lengths of the legs and the hypotenuse of one triangle must be equal to the corresponding sides of the other triangle.

In summary, two right-angled triangles are similar if they have the same angles (which can be determined by having another equal acute angle) or if their corresponding sides are proportional. Both conditions essentially indicate that the triangles have the same shape, just possibly different sizes.