A triangle PQR given that QR = 3cm, ∠PQR = 45° and QP - PR = 2 cm. Construct the following and give justification
Solution:
It is given that in triangle PQR,
QR = 3cm
∠ PQR = 45°
QP - PR = 2 cm
C lies on perpendicular bisector RS of AY
Steps of Construction
1. Construct the base QR of 3 cm length
2. Construct ∠XQR = 45° at point Q of the base QR
3. Now cut the line segment QS = QP - PR = 2 cm from the ray QX
4. Join SR and construct the perpendicular bisector of SR say AB
5. Let AB intersect QX at the point P
6. Join PR
7. Triangle PQR is the required triangle
Justification:
∠PQR and base QR are drawn
P lies on perpendicular bisector of SR
PS = PR
QS = PQ - PS
QS = PQ - PR
Therefore, the construction is justified.
✦ Try This: Construct each of the following and give justification: A triangle PQR given that QR = 4cm, ∠ PQR = 65° and QP - PR = 3 cm.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 11
NCERT Exemplar Class 9 Maths Exercise 11.4 Problem 2
A triangle PQR given that QR = 3cm, ∠PQR = 45° and QP - PR = 2 cm. Construct the following and give justification
Summary:
A triangle PQR given that QR = 3cm, ∠ PQR = 45° and QP - PR = 2 cm is constructed and justified
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