NCERT solution Class 8 understanding quadrilaterals

NCERT Solutions

Class 8 Maths

Understanding Quadrilaterals

NCERT Questions

Ex. 3.1 Q1.
Ex. 3.1 Q2.
Ex. 3.1 Q3.
Ex. 3.1 Q4.
Ex. 3.1 Q5.
Ex. 3.1 Q6.
Ex. 3.1 Q7.
Ex. 3.2 Q1.
Ex. 3.2 Q2.
Ex. 3.2 Q3.
Ex. 3.2 Q4.
Ex. 3.2 Q5.
Ex. 3.2 Q6.
Ex. 3.3 Q1.
Ex. 3.3 Q2.
Ex. 3.3 Q3.
Ex. 3.3 Q4.
Ex. 3.3 Q5.
Ex. 3.3 Q6.
Ex. 3.3 Q7.
Ex. 3.3 Q8.
Ex. 3.3 Q9.
Ex. 3.3 Q10.
Ex. 3.3 Q11.
Ex. 3.3 Q12.
Ex. 3.4 Q1.
Ex. 3.4 Q2.
Ex. 3.4 Q3.
Ex. 3.3 Q4.
Ex. 3.4 Q5.
Ex. 3.4 Q6.

Ex. 3.1 Q3.

What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try)

Let ABCD is a convex quadrilateral, then we draw a diagonal AC which divides the quadrilateral in two triangles.

Ð A + ÐB + Ð C + Ð D = Ð 1 + Ð 6 + Ð 5 + Ð 4 + Ð 3 + Ð 2

= (Ð 1 + Ð 2 + Ð 3) + (Ð 4 + Ð 5 + Ð 6)

= 180⁰ + 180⁰ [By Angle sum property of triangle]

= 360⁰

Hence, the sum of measures of the triangles of a convex quadrilateral is 360⁰.

Yes, if quadrilateral is not convex then, this property will also be applied.

Let ABCD is a non-convex quadrilateral and join BD, which also divides the quadrilateral in two triangles.

Using angle sum property of triangle,

In Δ ABD, Ð 1 + Ð 2 + Ð 3 = 180⁰ …………….1

In Δ BDC, Ð 4 + Ð 5 + Ð 6 = 180⁰ …………….2

Adding equation 1 and 2, we get

Ð 1 + Ð 2 + Ð 3 + Ð 4 + Ð 5 + Ð 6 = 180⁰ + 180⁰

=> Ð 1 + Ð 2 + Ð 3 + Ð 4 + Ð 5 + Ð 6 = 360⁰

=> Ð A + ÐB + Ð C + Ð D = 360⁰

Hence proved.

Understanding Quadrilaterals Class 8 Maths NCERT Chapter 3 NCERT Solutions

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Attempt All Questions: Make an effort to attempt all the questions provided in the NCERT textbook. This comprehensive practice will help you cover the entire syllabus and reinforce your understanding across various topics. You may refer Class 8 Maths Understanding Quadrilaterals Online Test on LearnoHub.com.
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NCERT solutions of Understanding Quadrilaterals Class 8 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 8 Maths Understanding Quadrilaterals NCERT solutions.