Question

Draw a triangle ABC, with AC = 4 cm, BC = 3 cm and ∠C = 105°. Measure AB. Is (AB)² = (AC)² + (BC)²? If not, which one of the following is true:
(AB)² > (AC)² + (BC)² or (AB)² < (AC)² + (BC)²?

Answer 1

Draw $△ABC$.
Draw a line BC = 3 cm.
At point C, draw a line at 105$°$ angle with BC.
Take an arc of 4 cm from point C, which will cut the line at point A.
Now, join AB, which will be approximately 5.5 cm.
$$\begin{gathered} A{C}^2+B{C}^2=4^2+3^2=9+16=25 \\ A{B}^2=5.5^2=30.25 \end{gathered}$$

(AB)² $\ne$ (AC)² + (BC)²

Here,

(AB)² > (AC)² + (BC)²