10

Q1. A triangle has ____________ components.

• 3
• 4
• 5
• 6

Solution

6 components - three angles and three sides

Q2. A student of class VII attempts to make a triangle of dimension 2 cm, 3 cm and 6 cm. He drew the longest side first, thereby generating two vertices of the triangle. He could not get the third vertex. What could be the reason? 

• The sum of two sides is less than the third side
• No angle of the triangle is given
• The first step is wrong
• He does not know to draw the arc

Solution

In any triangle the sum of two sides is greater than the third side. With the given dimensions, the sum of two sides is less than the third side, i.e. 2 + 3 < 6, hence the triangle cannot be constructed.

Q3. The exterior angle of a triangle is equal in measure to the ______________ of interior opposite angles.

• Difference
• Sum
• Product
• None of these

Solution

Sum of the interior opposite angles - property of triangle.

Q4. Things required for accurate construction a triangle are

• Pencil, Ruler
• Pencil, Ruler, compass
• Pencil, Ruler, compass, protractor
• Only pencil

Solution

Pencil will be required as an instrument to draw. Ruler will be required to draw a straight line as well as measure the line. Compass will be required to make arc so as to draw angle/line bisectors. Protractor will be required for angle measurements.

Q5. If measure of one side is given, which of the following triangle can be constructed?

• Right-angled triangle
• Isosceles triangle
• Equilateral triangle
• Scalene triangle

Solution

Equilateral triangle as measure of all the three sides is same.

Q6. Which of the following information is not sufficient to construct a unique triangle?

• The three sides of the triangle are 3 cm, 5 cm and 7 cm
• Two sides and included angle of the triangle are 4 cm, 5 cm and 60⁰
• The measure of two angles and included side of the triangle
• The measure of three angles of the triangle are 50⁰, 60⁰ and 70⁰

Solution

To construct a triangle we should have at least one side given, there can be multiple triangles with three angles of measure 50⁰, 60⁰ and 70⁰.

Q7. In a right-angled triangle, the measure of ____________ angle/angles is 90^o.

• One
• Two
• Three
• None of these

Solution

In a right-angled triangle, only one angle is of measure 90^o.

Q8. Which of the following represent a pair of parallel lines?

• Railway Tracks
• Crossroads
• Spokes of wheel
• Sun Rays

Solution

Railway Tracks

Q9. Arav was asked to construct a triangle ABC with sides AB and BC equal to 5 cm and 6.5 cm respectively. The measure of the angle B is 60⁰. He started the construction, which of the following steps of construction followed by him is incorrect

• Draw a line segment BC of length 6.5 cm
• At point C draw an angle XCB = 60⁰
• With point B as centre and radius 5 cm draw an arc, which cuts line XB at point A.
• Join AB, Triangle ABC so formed is the required triangle.

Solution

Since the measure of angle B is 60⁰, he should have drawn angle 60⁰ at point B and not at C.

Q10. The steps of construction of an isosceles triangle PQR with angle PQR as 110^o are as follows: (i)     Draw the base QR. (ii)    Join P to R to obtain the required triangle PQR. (iii)   At point Q, draw a ray QX making an angle 110° with QR. (iv)   Taking Q as centre, draw an arc of radius equal to QR. It intersects QX at the point P. The correct order of steps is

• (i), (ii), (iii), (iv)
• (i), (iii), (iv), (ii)
• (i), (iv), (ii), (iii)
• (i), (iii), (ii), (iv)

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