Question

How to describe congruent triangles?

Answer 1

Congruency is a term used to describe two objects with the same shape and size.

In this case, two triangles are congruent if they have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position.

For instance,

these triangles are congruent. They have the same sides but in different position.

Another example is

In this case the congruency is about angles. These 2 triangles have the same angles and the same sides but in different positions.

Another instance is

They are the same triangles but in different positions.

From the first question we can see that both triangles are congruent.

This imply that they are the same but in different position:

We can note that angle C is equal to angle T, therefore

`\angle T=55`

In the same way, angle U is equal to angle B, then we have

`\angle B=59`

We can find angle A by noticing that the interior angles of a triangle add up 180, that is

`\begin{gathered} \angle A+\angle B+\angle C=180 \\ \angle A+59+55=180 \\ \angle A+114=180 \\ \angle A=180-114 \\ \angle A=66 \end{gathered}`

Since angle V is equal to angle A, also V=66