GSEB Class 7 Maths Solutions Chapter 10 Practical Geometry Exercise 10.3

Question 1. Construct ΔDEF such that DE = 5 cm, DF = 3 cm and m∠EDF = 90°.
Answer:
Steps of construction:
I. Create a line segment DE, measuring 5 cm.
II. At point D, draw angle EDX to be 90 degrees.
III. From the line DX, mark off segment DF, which is 3 cm long.
IV. Connect points E and F.
This creates triangle DEF, which is the desired shape.

Exam Tip: When constructing triangles using the SAS (Side-Angle-Side) criterion, always begin by drawing the given side, then the angle at the vertex, and finally the second side.

Question 2. Construct an isosceles triangle in which the lengths of each of its equal sides is 6.5 cm and the angle between them is 110°.
Answer:
Steps of construction:
I. Make a line segment AB that measures 6.5 cm.
II. From point B, using a protractor, construct an angle ABX that is 110 degrees.
III. Along the ray BX, measure and mark BC, making it 6.5 cm long.
IV. Connect point C to point A.
Therefore, triangle ABC is the isosceles triangle we needed to build.

Exam Tip: Remember that an isosceles triangle has two sides of equal length. Ensure you draw both given sides with the correct measurement and the angle between them accurately.

Question 3. Construct ΔABC with BC = 7.5 cm, AC = 5 cm and m∠C = 60°.
Answer:
Steps of construction:
I. Draw a line segment BC, measuring 7.5 cm.
II. At point C, construct an angle BCX that is 60 degrees.
III. Along the ray CX, mark off segment CA, making it 5 cm long.
IV. Connect points A and B.
This forms triangle ABC, which is the triangle we wanted.

Exam Tip: When constructing a triangle with two sides and the included angle (SAS), accurately measuring the angle at the correct vertex is crucial for a precise outcome.