GSEB Class 7 Maths Solutions Chapter 10 પ્રાયોગિક ભૂમિતિ Exercise 10.3

Question 1. DE = 3 સેમી, DP = 3 સેમી અને \( m\angle \mathbf{E D F} = 90° \) ડોય તેવો \( \triangle DEF \) ૨યો.
Answer:

Construction Points:
1. Draw a line segment DE with a length of 5 cm.
2. Using a ruler and compass, draw a ray DA at point D on \overline{\mathrm{DE}} such that \( m\angle \mathbf{E D F} = 90° \).
3. Using a ruler and compass, find a point F on \overrightarrow{\mathrm{DA}} so that DF equals 3 cm.
4. Draw the line segment \overline{\mathrm{FE}}.
Therefore, \( \triangle DEF \) is the required triangle.
In simple words: First, draw the base line. Then, make a perfect corner angle at one end. Measure the other side along that angle's line and connect the final point to the base.

Exam Tip: For constructing a right-angled triangle with two sides, always start by drawing the base. Then, construct the 90-degree angle at the correct vertex before measuring the second side along that perpendicular line.

Question 2. એક સમદ્વિબાજુ ત્રિકોણ રચો જેમાં બંને સમાન બાજુનાં માપ 6.5 સેમી અને તેમની વચ્ચેનો ખૂણો 110°નો હોય.
Answer:

Construction Points:
1. Draw a line segment \overline{\mathrm{EF}} that is 6.5 cm long.
2. Using a protractor, draw a ray \overrightarrow{\mathrm{FX}} at point F on \overline{\mathrm{EF}} to make an angle of 110°.
3. Using a ruler and compass, find a point D on \overrightarrow{\mathrm{FX}} such that FD measures 6.5 cm.
4. Draw the line segment \overline{\mathrm{ED}}.
Thus, \( \triangle DEF \) is the required triangle.
In simple words: Start with the base length. At one end, make the given angle using a protractor. Measure the second equal side along this new line and connect the third point.

Exam Tip: When constructing an isosceles triangle using the SAS (Side-Angle-Side) criterion, ensure the given angle is indeed *between* the two equal sides. Mark the lengths carefully on the construction.

Question 3. BC = 7.5 સેમી, AC = 5 સેમી અને \( m\angle \mathbf{C} = 60° \) હોય તેવો \( \triangle ABC \) રચો.
Answer:

Construction Points:
1. Draw a line segment BC with a length of 7.5 cm.
2. At point C on \overline{\mathrm{BC}}, construct a ray \overrightarrow{\mathrm{CX}} using a ruler and compass, forming a 60° angle.
3. Using a ruler and compass, get a point A on \overrightarrow{\mathrm{CX}} such that CA measures 5 cm.
4. Draw the line segment AB.
Therefore, \( \triangle ABC \) is the required triangle.
In simple words: First, draw the longest side as the base. At one end of this base, make the given angle. Then, mark the length of the second side along this angled line, and finally, join the remaining two points.

Exam Tip: Always double-check that the angle you construct is at the correct vertex and that the sides adjacent to it are of the specified lengths. Accuracy in measurement is key for full marks.