Question

Draw any acute $\Delta ACU$. Use a method based on the $SSS$ postulate to construct a triangle congruent to $\Delta ACU$.

Short answer

By $SSS$congruency $\Delta PQR\cong \Delta ACU$.

Step-by-step solution

Step 1. Given information.

An acute$\Delta ACU$ is given.

Step 2. Draw the acute triangle.

Acute$\Delta ACU$ is drawn below.

Here, $\Delta ACU$ is an acute triangle as each of the angle has measure less than $90°$.

Step 3. Concept used.

According to $SSS$ congruence criteria,

if all the sides of one triangle are congruent to the corresponding sides of other triangle,

then the two triangles are said to be congruent.

Step 4. Construct the congruent triangle.

Construct $\Delta PQR$such that $PQ\cong AC, PR\cong AU, QR\cong CU$.

So,

$\Delta PQR\cong \Delta ACU$ (by $SSS$congruence criteria)

Therefore,by $SSS$congruency $\Delta PQR\cong \Delta ACU$.