Exercise 8
(1) Fill in the blanks:
(i)
A triangle in which all three sides have the same length is called
triangle.
(ii)
A triangle in which only two sides have equal lengths is called
triangle.
(iii)
A triangle whose one angle is
degrees is called a right angled triangle.
(iv)
The line segment joining the vertices of the opposite angles of a quadrilateral is called a
of the quadrilateral.
(v)
In
L M N O,
side LM and side
are adjacent sides.
Solution — Question 1
Ans (i)
A triangle in which all three sides have the same length is called
equilateral triangle.
Ans (ii)
A triangle in which only two sides have equal lengths is called
isosceles triangle.
Ans (iii)
A triangle whose one angle is
90
degrees is called a right angled triangle.
Ans (iv)
The line segment joining the vertices of the opposite angles of a quadrilateral is called a
diagonal
of the quadrilateral.
Ans (v)
In
LMNO,
side LM and side
MN/LO
are adjacent sides.
(2) State whether true or false:
(i)
A triangle can have two right angles.
(ii)
A right angled triangle can be an isosceles triangle.
(iii)
An acute-angled triangle cannot be an equilateral triangle.
Solution — Question 2
Ans (i)
False.
Ans (ii)
True.
Ans (iii)
False.
(3) Draw
UVWX
and write the answers to the following questions from it:
(i)
Write the names of the quadrilateral in different ways.
(ii)
Write the pairs of opposite sides.
(iii)
Write the pairs of adjacent sides.
(iv)
Write the names of the diagonals.
(v)
Write the pairs of opposite angles.
(vi)
Write the pairs of adjacent angles.
Solution — Question 3
Ans (i)
Name of the quadrilaterals:
UVWX
,
VWXU
,
WXUV
,
XUVW
,
UXWV , XWVU , WVUX , VUXW .
UXWV , XWVU , WVUX , VUXW .
Ans (ii)
Pairs of opposite sides:
(1) seg UV and seg XW.(2) seg VW and seg UX.
Ans (iii)
Pairs of adjacent sides:
(1) seg VU and seg VW.(2) seg WV and seg WX.
(3) seg XW and seg XU.
(4) seg UX and seg UV.
Ans (iv)
Names of the diagonals:
(1) seg WU and (2) seg VX.
Ans (v)
Pairs of opposite angles:
(1)
U
and
W
.
(2) V and X .
Ans (vi)
Pairs of adjacent angles:
(1)
U
and
V
.
(2) V and W .
(3) W and X .
(4) X and U .
(4) How many triangles are there in the figure below?
(i)
(ii)
(iii)
(iv)
Solution — Question 4
Ans (i)
There are 3 triangles in figure (i).
Ans (ii)
There are 6 triangles in figure (ii).
Ans (iii)
There are 12 triangles in figure (iii).
Ans (iv)
There are 15 triangles in figure (iv).
(5) Count and write the total number of quadrilaterals in the adjacent figure.
Solution — Question 5
Ans
The figure has 6 vertical lines
and 5 horizontal lines.
To form a quadrilateral, we choose any 2 vertical lines and any 2 horizontal lines.
Number of ways to choose 2 vertical lines = 15.
Number of ways to choose 2 horizontal lines = 10.
∴ Total number of quadrilaterals
= 15 × 10
= 150.
To form a quadrilateral, we choose any 2 vertical lines and any 2 horizontal lines.
Number of ways to choose 2 vertical lines = 15.
Number of ways to choose 2 horizontal lines = 10.
∴ Total number of quadrilaterals
= 15 × 10
= 150.
Ans. There are 150 quadrilaterals.