Que-3 Draw 5 Convex and 5 Concave Polygons.
Que-4 Name and Draw 2 Regular and 2 Irregular polygons.
Que-5 Explain all the types of quadrilaterals (Parallelogram, Rhombus, Rectangle, Square, Kite and Trapezium) with their properties.
Please answer those questions....
Answers
Answer:
Question 1:
Given here are some figures:
Class_8_Understanding_Quadrilateral_DifferentFigures
Classify each of them on the basis of the following:
(a) Simple curve (b) Simple closed curve (c) Polygon (d) Convex polygon (e) Concave polygon
Answer:
(a) Simple curve
Class_8_Understanding_Quadrilateral_SimpleCurve
(b) Simple closed curve
Class_8_Understanding_Quadrilateral_SimpleClosedCurve
(c) Polygons
Class_8_Understanding_Quadrilateral_Polygon
(d) Convex polygons
Class_8_Understanding_Quadrilateral_ConvexPolygon
(e) Concave polygon
Class_8_Understanding_Quadrilateral_ConcavePolygon
Question 2:
How many diagonals does each of the following have?
(a) A convex quadrilateral (b) A regular hexagon (c) A triangle
Answer:
(a) A convex quadrilateral has two diagonals.
Class_8_Understanding_Quadrilateral_ConvexQuadrilateral
Here, AC and BD are two diagonals.
(b) A regular hexagon has 9 diagonals.
Class_8_Understanding_Quadrilateral_RegularHexagon
Here, diagonals are AD, AE, BD, BE, FC, FB, AC, EC and FD.
(c) A triangle has no diagonal.
Question 3:
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)
Answer:
Let ABCD is a convex quadrilateral, then we draw a diagonal AC which divides the quadrilateral
in two triangles.
Class_8_Understanding_Quadrilateral_ConvexQuadrilateral1
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.
Class_8_Understanding_Quadrilateral_NonConvexQuadrilateral1
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.
Question 4:
Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)
Class_8_Understanding_Quadrilateral_ConvexPolygons
What can you say about the angle sum of a convex polygon with number of sides?
Answer:
(a) When n = 7, then
Angle sum of a polygon = (n - 2) * 1800 = (7 - 2) * 1800 = 5 * 1800 = 9000
(b) When n = 8, then
Angle sum of a polygon = (n - 2) * 1800 = (8 - 2) * 1800 = 6 * 1800 = 10800
(c) When n = 10, then
Angle sum of a polygon = (n - 2) * 1800 = (10 - 2) * 1800 = 8 * 1800 = 14400
(d) When n = n, then
Angle sum of a polygon = (n - 2) * 1800
Question 5:
What is a regular polygon? State the name of a regular polygon of:
(a) 3 sides (b) 4 sides (c) 6 sides
Answer:
A regular polygon: A polygon having all sides of equal length and the interior angles of
equal size is known as regular polygon.
(i) 3 sides
Polygon having three sides is called a triangle.
(ii) 4 sides
Polygon having four sides is called a quadrilateral.
(iii) 6 sides
Polygon having six sides is called a hexagon.
Question 6:
Find the angle measures x in the following figures:
Class_8_Understanding_Quadrilateral_DifferentFigures1
Answer:
(a) Using angle sum property of a quadrilateral,
500 + 1300 + 1200 + 3600 + x = 3600
=> 3000 + x = 3600
=> x = 3600 – 3000
=> x = 600
Class_8_Understanding_Quadrilateral_Quadrilateral3
(b) Using angle sum property of a quadrilateral,
900 + 600 + 700 + x = 3600
=> 2200 + x = 3600
=> x = 3600 - 2200
=> x = 1400
Class_8_Understanding_Quadrilateral_Quadrilateral4
(c) First base interior angle = 1800 – 700 = 1100
Second base interior angle = 1800 - 600 = 1200
There are 5 sides, n = 5
Angle sum of a polygon = (n - 2) * 1800
= (5 - 2) * 1800
= 3 * 1800
= 5400
So, 300 + x + 1100 + 1200 + x = 5400
=> 2600 + 2x = 5400
=> 2x = 5400 – 2600
=> 2x = 2800
=> x = 2800/2
=> x = 1400
Class_8_Understanding_Quadrilateral_Quadrilateral5
(d) Angle sum of a polygon = (n - 2) * 1800
= (5 - 2) * 1800
= 3 * 1800
= 5400
Now, x + x + x + x + x = 5400
=> 5x = 5400
=> x = 5400/5
=> x = 1080
Hence each interior angle is 1080.
Class_8_Understanding_Quadrilateral_Polygon1
Answer:
Question 1:
Given here are some figures:
Class_8_Understanding_Quadrilateral_DifferentFigures
Classify each of them on the basis of the following:
(a) Simple curve (b) Simple closed curve (c) Polygon (d) Convex polygon (e) Concave polygon
Answer:
(a) Simple curve
Class_8_Understanding_Quadrilateral_SimpleCurve
(b) Simple closed curve
Class_8_Understanding_Quadrilateral_SimpleClosedCurve
(c) Polygons
Class_8_Understanding_Quadrilateral_Polygon
(d) Convex polygons
Class_8_Understanding_Quadrilateral_ConvexPolygon
(e) Concave polygon
Class_8_Understanding_Quadrilateral_ConcavePolygon
Question 2:
How many diagonals does each of the following have?
(a) A convex quadrilateral (b) A regular hexagon (c) A triangle
Answer:
(a) A convex quadrilateral has two diagonals.
Class_8_Understanding_Quadrilateral_ConvexQuadrilateral
Here, AC and BD are two diagonals.
(b) A regular hexagon has 9 diagonals.
Class_8_Understanding_Quadrilateral_RegularHexagon
Here, diagonals are AD, AE, BD, BE, FC, FB, AC, EC and FD.
(c) A triangle has no diagonal.
Question 3:
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)
Answer:
Let ABCD is a convex quadrilateral, then we draw a diagonal AC which divides the quadrilateral
in two triangles.
Class_8_Understanding_Quadrilateral_ConvexQuadrilateral1
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.
Class_8_Understanding_Quadrilateral_NonConvexQuadrilateral1
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.
Question 4:
Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)
Class_8_Understanding_Quadrilateral_ConvexPolygons
What can you say about the angle sum of a convex polygon with number of sides?
Answer:
(a) When n = 7, then
Angle sum of a polygon = (n - 2) * 1800 = (7 - 2) * 1800 = 5 * 1800 = 9000
(b) When n = 8, then
Angle sum of a polygon = (n - 2) * 1800 = (8 - 2) * 1800 = 6 * 1800 = 10800
(c) When n = 10, then
Angle sum of a polygon = (n - 2) * 1800 = (10 - 2) * 1800 = 8 * 1800 = 14400
(d) When n = n, then
Angle sum of a polygon = (n - 2) * 1800
Question 5:
What is a regular polygon? State the name of a regular polygon of:
(a) 3 sides (b) 4 sides (c) 6 sides
Answer:
A regular polygon: A polygon having all sides of equal length and the interior angles of
equal size is known as regular polygon.
(i) 3 sides
Polygon having three sides is called a triangle.
(ii) 4 sides
Polygon having four sides is called a quadrilateral.
(iii) 6 sides
Polygon having six sides is called a hexagon.
Question 6:
Find the angle measures x in the following figures:
Class_8_Understanding_Quadrilateral_DifferentFigures1
Answer:
(a) Using angle sum property of a quadrilateral,
500 + 1300 + 1200 + 3600 + x = 3600
=> 3000 + x = 3600
=> x = 3600 – 3000
=> x = 600
Class_8_Understanding_Quadrilateral_Quadrilateral3
(b) Using angle sum property of a quadrilateral,
900 + 600 + 700 + x = 3600
=> 2200 + x = 3600
=> x = 3600 - 2200
=> x = 1400
Class_8_Understanding_Quadrilateral_Quadrilateral4
(c) First base interior angle = 1800 – 700 = 1100
Second base interior angle = 1800 - 600 = 1200
There are 5 sides, n = 5
Angle sum of a polygon = (n - 2) * 1800
= (5 - 2) * 1800
= 3 * 1800
= 5400
So, 300 + x + 1100 + 1200 + x = 5400
=> 2600 + 2x = 5400
=> 2x = 5400 – 2600
=> 2x = 2800
=> x = 2800/2
=> x = 1400
Class_8_Understanding_Quadrilateral_Quadrilateral5
(d) Angle sum of a polygon = (n - 2) * 1800
= (5 - 2) * 1800
= 3 * 1800
= 5400
Now, x + x + x + x + x = 5400
=> 5x = 5400
=> x = 5400/5
=> x = 1080
Hence each interior angle is 1080.
Class_8_Understanding_Quadrilateral_Polygon1