Chapter 4.5, Problem 5WE

To determine

To prove $\Delta \text{AOB}\cong \Delta \text{AOC}$

Answer to Problem 5WE

  $\Delta \text{AOB}\cong \Delta \text{AOC}$

Explanation of Solution

Given Information

  $\overrightarrow{\text{AO}}\perp \text{plane}M\text{,}$

And also, $\text{BO}\cong \text{CO}$

Proof

Considering the given figure, we will:

  

Considering $\Delta \text{AOB}$ and $\Delta \text{AOC}$ of which sides, BO and OC lies on plane $M$

	Points	Reasons
(i)	$\text{BO}\cong \text{CO}$	Given
(ii)	$\angle \text{AOB}\cong \angle \text{AOC}$	$\overrightarrow{\text{AO}}\perp$plane $M$M,So, $\text{AO}\perp \text{BO }$and $\text{AO}\perp \text{OC}$
(iii)	$(\text{AO}=\text{OA})$	Common in both triangles

So, by SAS congruency,

  $\Delta \text{AOB}\cong \Delta \text{AOC}$