91影视

Two triangles are said congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. Congruent triangles are triangles that have same size and shape.

The two triangles are said to be congruent if they are copies of each other and if their vertices are superposed, then say that corresponding angles and the sides of the triangles are congruent.

Congruency of triangles can be proved by SSS, SAS and ASA, AAS and HL postulates.

To prove that two segments or two angles are congruent, firstly identity the two triangles in which that two segments or angles are corresponding parts. After that, prove that the identified triangles are congruent and then, state that the two parts are congruent using the reason 鈥淐orresponding parts of $鈮�$triangles are $鈮�$鈥�.

Now draw a rough figure using the information in the problem.

As, $\stackrel{炉}{AX}$ is the median and altitude of $螖ABC$, So $\stackrel{炉}{BX}=\stackrel{炉}{XC}$ and $m鈭�AXB=m鈭�AXC=90$. This implies; $\stackrel{炉}{BX}=\stackrel{炉}{XC}$ and $鈭�AXB=鈭�AXC$ by definition of congruent segments and angles. Also $\stackrel{炉}{AX}鈮�\stackrel{炉}{AX}$ by reflexive property and thus, $螖AXB鈮�螖AXC$ by SAS postulate. Therefore, $\stackrel{炉}{AB}$and $\stackrel{炉}{AC}$ are corresponding parts of congruent triangles. Thus, $螖ABC$ is isosceles by definition of isosceles triangle.

Therefore,$螖ABC$ is isosceles by definition of isosceles triangle.