If one acute angle is double than the other in a right-angled triangle, prove that the hypotenuse is double the smallest side.
Answer:
- Let be the right-angled triangle with and .
Let be equal to . So, - We see that is the hypotenuse of .
Also, the side opposite to the smallest angle is the smallest. Thus, is the smallest side.
Now, we need to prove . - Let us extend to such that and join point to point .
- In and , we have
- As corresponding parts of congruent triangles are equal, we have
- Now, in , we have
- .