Draw a `DeltaABC` with `angleC=90^(@)`, hypotenuse Ab = 5 cm and side AC = 4 cm. Also, draw a `DeltaPQR` with `angleR=90^(@)`, hypotenus PQ = 5 cm and side PR = 4 cm.
State about the congruency of triangles.

Answer

To solve the problem, we need to draw two right triangles, \( \Delta ABC \) and \( \Delta PQR \), and then determine their congruency. Let's go through the steps one by one.

### Step-by-Step Solution:

**Step 1: Draw Triangle \( \Delta ABC \)**
1. Start by drawing a right angle at point \( C \).
2. Label the right angle as \( \angle C = 90^\circ \).
3. From point \( C \), draw line segment \( AC \) measuring 4 cm.
4. Now, draw the hypotenuse \( AB \) measuring 5 cm. To do this, use a compass or ruler to ensure the length is accurate.
5. Finally, connect points \( A \) and \( B \) to complete triangle \( ABC \).

**Step 2: Draw Triangle \( \Delta PQR \)**
1. Similarly, draw a right angle at point \( R \).
2. Label the right angle as \( \angle R = 90^\circ \).
3. From point \( R \), draw line segment \( PR \) measuring 4 cm.
4. Now, draw the hypotenuse \( PQ \) measuring 5 cm.
5. Connect points \( P \) and \( Q \) to complete triangle \( PQR \).

**Step 3: Analyze the Congruency of Triangles**
1. Both triangles \( \Delta ABC \) and \( \Delta PQR \) have a right angle (90 degrees).
2. The hypotenuse \( AB \) of triangle \( ABC \) is equal to the hypotenuse \( PQ \) of triangle \( PQR \) (both are 5 cm).
3. The side \( AC \) of triangle \( ABC \) is equal to the side \( PR \) of triangle \( PQR \) (both are 4 cm).
4. Since both triangles have one right angle, one pair of equal sides (the hypotenuses), and another pair of equal sides, we can conclude that the triangles are congruent by the RHS (Right angle-Hypotenuse-Side) congruence criterion.

### Conclusion:
Thus, we can state that \( \Delta ABC \cong \Delta PQR \) by the RHS congruence criterion.

---