Question

S3. Construct a APQR with PQ = QR = 7 cm and ZPQR = 45°. What type of a triangle is APQR?​

Answer 1

Answer:

Isosceles Triangle

Third angle = 90° and pqr is an isosceles triangle. Now, In Δpqr the two sides are equal, so Δpqr is an isosceles triangle.

1.Draw base BC=7cm

2.Let's draw ∠B=75°.Let the ray be BX

3.Open the compass to length AB+AC=13cm.From point B as center, cut an arc on ray BX.Let the arc intersect BX at D

4.Join $$CD$

5.Now, we will draw perpendicular bisector of CD

6.Mark point A where perpendicular bisector intersects BD

7.Join AC

Result:△ABC is the required triangle.

Answer 2

Steps of construction :

1. Draw a ray OX and cut off a line segment QR = 3cm.

2. At Q, construction ∠ YQR = 45

∘

with the help of protractor .

3. On QY , cut off QS = 2cm.

4. Join RS.

5. Draw perpendicular bisector of RS to meet QY at P.

6. Join PR. Then PQR is the required triangle.