In Text Questions (Text Book Page No. 157,158,160,169,173,177,187,193,194,195,196) - Chapter 5 Geometry 8th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Answer the following questions by recalling the properties of triangles:
Question $1 .$
The sum of the three angles of a triangle is
Answer:
$180^{\circ}$
 

Question $2 .$
The exterior angle of a triangle is equal to the sum of the ____angles to it.
Answer:
interior

Question $3 .$
In a triangle, the sum of any two sides is ___ than the third side.
Answer:
greater

Question $4 .$
Angles opposite to equal sides are ___and vice - versa.
Answer:
Equal

Question $5 .$
What is $\angle \mathrm{A}$ in the triangle $\mathrm{ABC}$ ?

Answer:
The exterior angle $=$ sum of interior opposite angles.
$\therefore \angle \mathrm{A}+\angle \mathrm{C}=1500$ in $\triangle \mathrm{ABC}$
But $\angle C=40^{\circ}$
[ Vertically opposite angler are equal]
$\begin{aligned}
&\therefore \angle \mathrm{A}+\angle \mathrm{C}=150^{\circ} \\
&\Rightarrow \angle \mathrm{A}+\angle 40^{\circ}=150^{\circ} \\
&\angle \mathrm{A}=150^{\circ}-40^{\circ} \\
&\angle \mathrm{A}=1100
\end{aligned}$

Try These (Text Book page No. 157 )
Identify the pairs of figures which are similar and congruent and write the letter pairs.

Answer:
Similar shapes:
(i) Wand L
(ii) $\mathrm{B}$ and $]$
(iii) $A$ and $G$
(iv) $\mathrm{B}$ and $J$
(v) $B$ and $Y$
(vi) $E$ and $N$
(vii) II and $Q$
(viii) $R$ and $T$
(ix) $\mathrm{S}$ and T
Congruent shapes:
(i) $Z$ and I
(ii) $J$ and $Y$
(iii) $C$ and $P$
(iv) $B$ and $K$
(v) $R$ and $S$
(vi) I and $Z$
You can find more.

Try These (Text Book page No. 158)
Question $1 .$
Match the following by their congrucnce property

Answer:
1. - (iv),
2. - (iii).
3. - (i),
4. - (ii)
 

Think (Text Book page No. 160)
In the figur,, $\mathrm{DA}=\mathrm{DC}$ and $\mathrm{RA}=\mathrm{RC}$. Am the triangles $\mathrm{DRA}$ and $\mathrm{DRC}$ congnorn?? Why?

Answer:
Here $\mathrm{AD}=\mathrm{CD}$
$\mathrm{AB}=\mathrm{CB}$
$\mathrm{DB}=\mathrm{DB}$ (common)
$\triangle \mathrm{DB}=\triangle \mathrm{DBC}$
Also RHS rule also bind here to say their congruency.
 

Activity (Text Book page No. 169)
Question 1.
We can construct sets of Pythagorean triplets as follows.
Let $m$ and $n$ be any two positive integers $(m>n)$ :
$(a, b, c)$ is a Pythagorean triplet if $a=m^{2}-n^{2}, b=2 m n$ and $c=m^{2}+n^{2}$ (Think, why?) Complete the table.

Question $2 .$
Find all integer-sided right angled triangles with hypotenuse 85 .
Answer:
$\begin{aligned}
&(x+y)^{2}-2 x y=85^{2} \\
&13,84,85 \\
&36,77,85 \\
&40,75,85 \\
&51,68,85
\end{aligned}$

Think (Text Book page No. 173)
Question 1.
In any acute angled triangle, all three altitudes are inside the triangle. Where will be the orthocentre? In the interior of the triangle or in its exterior?

Answer:
Interior of the triangle
 

Question $2 .$
In any right angled triangle, the altitude perpendicular to the hypotenuse is inside the triangle; the other two altitudes are the legs of the triangle. Can you identify the orthocentre in this casc?

Answer:
Vertex containing $90^{\circ}$
 

Question 3 .
In any obtuse angled triangle, the altitude connected to the obtuse vertex is inside the triangle, and the two altitudes connected to the acute vertices are outside the triangle. Can you identify the orthocentre in this case?
Altitude of an obtuse triangle
Answer:
Exterior of the triangle.

Try These (Text Book page No. 177)
Identify the type of segment required in each triangle:
(median, altitude, perpendicular bisector, angle bisector)

Think (Text Book page No. 187)
Is it possible to construct a quadrilateral $\mathrm{PQRS}$ with $\mathrm{PQ}=5 \mathrm{~cm}, \mathrm{QR}=3 \mathrm{~cm}, \mathrm{RS}=6 \mathrm{~cm}, \mathrm{PS}=7 \mathrm{~cm}$ and $\mathrm{PR}=10 \mathrm{~cm}$. If not, why?

Answer:

The lower triangle cannot be constructed as the sum of two sides $5+3=8<10 \mathrm{~cm}$. So this quadrilateral cannot be constructed,
 

Try These (Text Book page No. 187)
Question $1 .$
The area of the trapezium is
Answer:
$\frac{1}{2} \times h \times(a+b)$ sq. units
 

Question $2 .$
The distance between the parallel sides of a trapezium is called as
Answer:
its height

Question $3 .$
If the height and parallel sides of a trapezium are $5 \mathrm{~cm}, 7 \mathrm{~cm}$ and $5 \mathrm{~cm}$ respectively, then
its area is
Answer:
30
Hints:
$\begin{aligned}
&=\frac{1}{2} \times h \times(a+b) \text { sq. units } \\
&=\frac{1}{2} \times 5 \times(7+5)=\frac{1}{2} \times 5 \times 12=30 \mathrm{sq} . \mathrm{cm}
\end{aligned}$

Question $4 .$
In an isosceles trapezium, the non-parallel sides are in ___ length.
Answer:
equal

Question $5 .$
To construct a trapezium,___ measurements are enough.
Answer:
Four

Question $6 .$
If the area and sum of the parallel sides are $60 \mathrm{~cm}^{2}$ and $12 \mathrm{~cm}$, its height is
Answer:
$10 \mathrm{~cm}$
Hint:
Arca of the trapezium $=\frac{1}{2} \times \mathrm{h}(\mathrm{a}+\mathrm{b})$
$$
\begin{aligned}
&60=\frac{1}{2} \times \mathrm{h} \times(12) \\
&\therefore \mathrm{h}=\frac{60 \times 2}{12}=10 \mathrm{~cm}
\end{aligned}$

Activity (Text Book page No. 193 \& 194)
Question I.
A pair of identical $30^{\circ}-60^{\circ}-90^{\circ}$ set-squares are needed for this activity. Place them as shown in the figure.

(i) What is the shape we get? It is a parallelogram.
Answer:
(ii) Are the opposite sides parallel?
Answer:
Yes
(iii) Are the opposite sides equal?
Ans:
Yes
(iv) Are the diagonals equal?
Answer:
No
(v) Can you get this shape by using any other pair of identical set-squares?
Answer:
Yes

Question 2 .
We need a pair of $30^{\circ}-60^{\circ}-90^{\circ}$ set- squares for this activity. Place them as shown in the figure.

(i) What is the shape we get"?
Ans:
Rectangle
(ii) Is it a parallelogram?
Answer:
Yes
(iii) It is a quadrilateral; infact it is a rectangle. (How?)
Ans:
Opposits sides are cqual.
All angles $=90^{\circ}$
(iii) What can we say about its lengths of sides, angles and diagonals?
Discuss and list them out.
Answer:
Opposite sides are equal
All angles are equal and are $=90^{\circ}$
Diagonals are equal

Question $3 .$
Repeat the above activity, this time with a pair of $45^{\circ}-45^{\circ}-90^{\circ}$ set-squares.

(i) How does the figure change now? Is it a parallelogram? It becomes a square! (How did it happen?)
Ans:
All sides are equal
(ii) What can we say about its lengths of sides, angles and diagonals? Discuss and list them out.
Answer:
All sides are equal
All angles $=90^{\circ}$
Diagonals equal
(iii) How does it differ from the list we prepared for the rectangle?
Answer:
All sides are equal.
Diagonals bisects each other.
 

Question $4 .$
We again use four Identical $30^{\circ}-60^{\circ}-90^{\circ}$ set- squares for this activity.
Note carcfully how they are placed touching one another.

(j) Do we get a parallelogram now?
Answer:
Yes
(ii) What can we say about its lengths of sides, angles and diagonals"?
Answer:
All sides equal.
opposaite sides arc cqual and parallel.
(iii) What is special about their diagonals?
Answer:
Diagonals bisects perpendicularly.
 

Try These (Text Book Page No. 195 \& 196)
Question 1.
Say True or False:
(a) A square is a special rectangle.
Answer:
True
(b) A square is a parallelogram.
Answer:
True
(c) A square is a special rhombus.
Answer:
True
(d) A rectangle is a parallelogram
Answer:
True

Question $2 .$
Name the quadrilaterals
(a) Which have diagonals bisecting each other.
Answer:
Square, rectangle, parallelogram, rhombus.
(b) In which the diagonals are perpendicular bisectors of each other.
Answer:
Rhombus and square.
(c) Which have diagonals of different lengths.
Answer:
Parallelogram and Rhombus
(d) Which have equal diagonals.
Answer:
Rectangle, square.
(c) Which have parallel opposite sides.
Answer:
Square, Rectangle. Rhombus, parallelogram.
(f) In which opposite angles are equal.
Answer:
Square, rectangle. rhombus, parallelogram

Question $3 .$
Two sticks are placed on a ruled sheet as shown. What figure is formed if the four corners of the sticks are joined?
(a)
Two unequal sticks. Placed such that their midpoints coincide.
Answer:
parallelogram

Two equal sticks. Placed such that their midpoints coincide.
Answer:
Rectangle

Two unequal sticks. Placed intersecting at mid points perpendicularly.
Answer:
Rhombus

Two equal sticke Placed interserting at mid points perpendicularly
Answer:
Square

Two uncqual sticks. Tops are not on the same ruling. Bottoms on the same ruling. Not cutting at the mid point of either. Answer:
Quadrilateral

Two unequal sticks. Tops on the same ruling. Bottoms on the same ruling. Not necessarily cutting at the mid point of either.
Answer:
Trapezium