Question

Column A	Column B
(i) Equilateral triangle, Isosceles triangle, Scalene triangle	(a) $∆ ABC ≅ ∆ FDE$
(ii) In a right-triangle, ${(Hypotenuse)}^{2} = (Sum of the squares of other two sides)$	(b) Pythagoras theorem
(iii) Acute-angled triangle, Obtuse-angled triangle, Right-angled triangle	(c) $∆ ABC ≅ ∆ EFD$
(iv) In $∆ ABC$ and $∆ DEF$ , we have $AB = FD, BC = DE, AC = FE, ∠ A = ∠ F$ .	(d) Types of triangles on the basis on their sides.
(v) In $∆ ABC$ and $∆ DEF$ , we have $BC = FD, AC = ED$ and $∠ C = ∠ D$ .	(e) Types of triangles on the basis of their angles.

Accepted Answer

We know that,

An equilateral triangle has all the sides equal.

An Isosceles triangle has two sides equal and the scalene triangle has all the sides different.

Hence, (i) $\to (d)$

We know that,

If the triangle is right angle triangle then by Pythagoras theorem,

${(Hypotenuse)}^{2} = {(Base)}^{2} + {(Perpendicular)}^{2}$

Thus, (ii) $\to (b)$

We know that,

A triangle having all angles less than $90^{o}$ is known as acute angle.

A triangle having angle greater than $90^{o}$ is known obtuse angle and a triangle in which one angle is $90^{o}$ is known as right angle triangle.

Thus, (iii) $\to (e)$

Consider the figures

and

As, $AB = FD, BC = DE$ , $AC = FE$ and $∠ A = ∠ F$

Hence, by SSS test $∆ ABC ≅ ∆ FDE$

Thus, (iv) $\to (a)$

Consider the figure,

and

As $BC = FD, AC = ED$ and $∠ C = ∠ D$

Hence, by SAS test

$∆ ABC ≅ ∆ EFD$

Thus, (v) $\to (c)$ .

Hence, we get

Column A Answer

(i) Equilateral triangle, Isosceles triangle, Scalene triangle
(d) Types of triangles on the basis of their sides.

(ii) In a right-triangle,

${(Hypotenuse)}^{2} = (Sum of the squares of other two sides)$
(b) Pythagoras theorem

(iii) Acute-angled triangle, Obtuse-angled triangle, Right-angled triangle (e) Types of triangles on the basis of their angles.

(iv) In $∆ ABC$ and $∆ DEF$ , we have $AB = FD, BC = DE, AC = FE, ∠ A = ∠ F$ . (a) $∆ ABC ≅ ∆ FDE$

(v) In $∆ ABC$ and $∆ DEF$ , we have $BC = FD, AC = ED$ and $∠ C = ∠ D$ . (c) $∆ ABC ≅ EFD$

ACROSS $\to$
1.	A ......... is a line that crosses at least two other lines.
2.	An ........... angle is more than $90 °$ but less than $180 °$ .
3.	An angle measuring $180 °$ is called a .......... angle.
	DOWN $↓$
4.	A ........... angle is an angle which is equal to $90 °$
5.	A line with definite end points is called a line ........... .
6.	A .......... angle is more than $180 °$ but less than $360 °$ .
7.	An ............ angle is more than $0 °$ but less than $90 °$ .

ACROSS $\to$
1.	The longest side of a right-angled triangle .........
2.	All the three sides of an equilateral triangle have same .......... .
3.	All the three sides of a .......... triangle are unequal.
	DOWN $↓$
4.	According to ........... theorem, in a right-angled triangle, ${(Hypotenuse)}^{2} = (Sum of the squares of other two sides)$
5.	An ............. triangle has two equal sides.
6.	The line segment joining a vertex and midpoint of the opposite side in a triangle is called a ........... .
7.	An ............ triangle has all the three sides equal.

ACROSS $\to$
1.	A quadrilateral having opposite sides parallel.
2.	A parallelogram with an angle of $90 °$ .
3.	A polygon having $4$ sides.
	DOWN $↓$
4.	A parallelogram having all sides congruent and each angle of $90 °$ .
5.	A quadrilateral with a pair of parallel sides.

ACROSS $\to$
1.	Vertical distance from bottom to top.
2.	The lowest part on which a thing stands or rests.
3.	A line at right angles to another.
4	Always remaining the same distance apart.
	DOWN $↓$
5.	The shorter side of a rectangle.
6.	A parallelogram having all of its sides equal such that none of the angles is $90 °$ .
7.	The line segment joining two opposite vertices of a quadrilateral.

ACROSS $\to$
1.	The midpoint of a diameter is at the point called
3.	Any segment connecting the centre of a circle to a point on the circle
4.	A portion of a circle
5.	A diameter divides the circle into two equal parts and each part is called:
	DOWN $↓$
2.	The path of all the points in a plane that are equidistant from a fixed point on the same plane.
6.	The longest chord of a circle:
7.	A line segment whose endpoints lie on the circumference of a circle.
8.	A polygon having its vertices at a circle is called:

Ram Chandra Solutions for Chapter: Geometry, Exercise 11: Enrichment Exercise

Ram Chandra Mathematics Solutions for Exercise - Ram Chandra Solutions for Chapter: Geometry, Exercise 11: Enrichment Exercise

Questions from Ram Chandra Solutions for Chapter: Geometry, Exercise 11: Enrichment Exercise with Hints & Solutions

Learn and Prepare for any exam you want !

Column A		Column B
(i)	Quadrilaterals with opposite pairs of sides are parallel.	(a)	Square
(ii)	A parallelogram having all sides congruent and diagonals bisecting at right angles.	(b)	Kite
(iii)	A parallelogram with all sides congruent and each angle equal to $90^{o}$ .	(c)	Trapezium
(iv)	A quadrilateral having two pairs of adjacent congruent sides.	(d)	Parallelogram
(v)	A quadrilateral having one pair of parallel sides.	(e)	Rhombus

Column A		Column B
(i)	An angle subtended by the diameter of the semicircle:	(a)	$180 °$
(ii)	Sum of opposite angles of a cyclic quadrilateral:	(b)	$80 °$
(iii)	$AB$ is a chord of a circle with centre $' O'$ and $OP = 3 cm$ . If radius is $5 cm$ then length of the chord $AB$ , when $OP ⊥ AB$ is:	(c)	$90 °$
(iv)	$ABCD$ is a cyclic quadrilateral in which $∠ BCD = 80 °$ . The measure of $∠ BAD$ is:	(d)	$100 °$
(v)	In a circle, chord $AB$ subtends $40 °$ at circle. The measure of angle subtended by it at centre is:	(e)	$8 cm$