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

We know that, A quadrilateral with opposite pairs of sides are parallel is known as a parallelogram. Thus, i → d We know that, A parallelogram having all sides congruent and diagonals bisecting at right angles is known as a rhombus. Thus, i i → e We know that, A parallelogram with all sides congruent and each angle equal to 90 ° is known as a square. Thus, i i i → a We know that, A quadrilateral having two pairs of adjacent congruent sides is known as a kite. Thus, i v → b We know that, A quadrilateral having one pair of parallel sides is known as trapezium. Thus, v → c Hence, we get Column A Answer (i) Quadrilaterals with opposite pairs of sides are parallel. (d) Parallelogram (ii) A parallelogram having all sides congruent and diagonals bisecting at right angles. (e) Rhombus (iii) A parallelogram with all sides congruent and each angle equal to 90 o . (a) Square (iv) A quadrilateral having two pairs of adjacent congruent sides. (b) Kite (v) A quadrilateral having one pair of parallel sides. (c) Trapezium

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

We know that, An angle subtended by the diameter of the semicircle is 90 ° . Thus, (i) → ( c ) We know, sum of the opposite angles of a cyclic quadrilateral is supplementary. So, sum of the opposite angles of a cyclic quadrilateral is 180 ° . Thus, (ii) → ( a ) Consider the figure, By using Pythagoras theorem, OA 2 = AP 2 + OP 2 5 2 = AP 2 + 3 2 AP 2 = 25 - 9 = 16 ∴ AP = 4 cm ....(by taking square root) As AB = 2 AP Hence, AB = 8 cm . Thus, (iii) → ( e ) Consider the figure, We know that, The sum of the opposite angles of the cyclic quadrilateral is 180 ° . So, ∠ BCD + BAD = 180 ° Hence, ∠ BAD = 180 ° - 80 ° = 100 ° Thus, (iv) → ( d ) Consider the figure, The measure of angle subtended by it at the centre is twice the angle subtended by the chord at the circle. From the figure, we get ∠ AOB = 2 × 40 ° ∴ ∠ AOB = 80 ° Thus, (v) → ( b ) Column A Answer (i) An angle subtended by the diameter of the semicircle: (c) 90 ° (ii) Sum of opposite angles of a cyclic quadrilateral: (a) 180 ° (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: (e) 8 cm (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 the centre is: (b) 80 °

Complete the following crossword puzzles, using the given hints. ACROSS → 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 ° .

We know, a transversal is a line that intersects at least two other lines. Hence, the required answer is transversal. We know, an angle that measures between 90 ° and 180 ° is known as obtuse angle. Hence, an obtuse angle is more than 90 ° but less than 180 ° . We know, an angle measuring 180 ° is called a straight angle. Hence, the required answer is a straight angle. We know, an angle that measures 90 ° is known as right-angle. We know a line segment is the shortest distance between two endpoints. Hence, a line with definite endpoints is called a line segment. Consider the figure, We know, a reflex angle is more than 180 ° but less than 360 ° . Thus, the required answer is reflex. We know, an angle measuring more than 0 ° but less than 90 ° is an acute angle. Hence, the required answer is acute. Hence, we get

Complete the following crossword puzzles, using the given hints. ACROSS → 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.

We know, in parallelogram opposite sides are always parallel. Hence, the required answer is a parallelogram. We know, the parallelogram is a rectangle with each angle measures 90 ° . Hence, the required answer is a rectangle. We know a polygon having 4 sides is known as a quadrilateral. Hence, the required answer is quadrilateral. We know, a parallelogram is a square having all the sides equal in measure and each angle is 90 ° . Hence, the required answer is square. We know, trapezium has one pair of parallel sides. Hence, the required answer is a trapezium.

Complete the following crossword puzzles, using the given hints. ACROSS → 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.

We know, height is measured from bottom to top. Hence, required answer is height. We know, the lowest part on which a thing stands or rest is known as base. Hence, required answer is base. We know, a line at right angles to another line is called perpendicular line. Hence, required answer is perpendicular. We know, parallel lines are lines that never intersect. Hence, required answer is parallel lines. We know, sides of rectangles are length and breadth in which breadth is smaller than length. Hence, required answer is breadth. A rhombus is a quadrilateral having all sides equal and it's not necessary that all the angles are 90 ° . Hence, required answer is rhombus. We know, diagonal is the line segment which joins two opposite sides of a quadrilateral. Hence, required answer is diagonal. Hence, we get

Complete the following crossword puzzles, using the given hints. ACROSS → 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:

We know that, The midpoint of a diameter is at the point which is known as centre. A diameter is the double of radius. Hence, the required answer is centre. We know that, any segment connecting the centre of a circle to a point on the circle is the radius. Radius is the half of diameter. Hence, the required answer is radius. We know that, a portion of a circumference of a circle is called arc. Hence, the required answer is arc. We know that, a diameter divides the circle into two equal parts and each part is called semicircle. The area of the semicircle is half of the area of the circle. Hence, the required answer is semicircle. We know that, the path of all the points in a plane that are equidistant from a fixed point on the same plane is called circle. The line segment that joins the centre of the circle with any point on the circle is called its radius. Hence, the required answer is circle. We know that, the longest chord of a circle is called diameter. It is double of radius. Hence, the required answer is diameter. We know that, a line segment whose endpoints lie on the circumference of a circle is called chord. Hence, the required answer is chord. We know that, a polygon having its vertices at circle is called cyclic. Hence, the required answer is cyclic. Therefore, we get

Angles in the same segment of a circle are equal

EASY

9th CBSE

IMPORTANT

Activity Plus in Mathematics>Chapter 4 - Geometry>Enrichment Exercise>Q A

A transversal is a line that intersects at least:

MEDIUM

9th CBSE

IMPORTANT

Activity Plus in Mathematics>Chapter 4 - Geometry>Enrichment Exercise>Q B

Area of a rhombus is equal to the product of its diagonals.

HARD

9th CBSE

IMPORTANT

Activity Plus in Mathematics>Chapter 4 - Geometry>Enrichment Exercise>Q C

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

HARD

9th CBSE

IMPORTANT

Activity Plus in Mathematics>Chapter 4 - Geometry>Enrichment Exercise>Q C

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)	$8 cm$

EASY

9th CBSE

IMPORTANT

Activity Plus in Mathematics>Chapter 4 - Geometry>Enrichment Exercise>Q D

Complete the following crossword puzzles, using the given hints.

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 $90 °$ .

Question Image

EASY

9th CBSE

IMPORTANT

Activity Plus in Mathematics>Chapter 4 - Geometry>Enrichment Exercise>Q D

Complete the following crossword puzzles, using the given hints.

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.

Question Image

EASY

9th CBSE

IMPORTANT

Activity Plus in Mathematics>Chapter 4 - Geometry>Enrichment Exercise>Q D

Complete the following crossword puzzles, using the given hints.

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.

Question Image

HARD

9th CBSE

IMPORTANT

Activity Plus in Mathematics>Chapter 4 - Geometry>Enrichment Exercise>Q D

Complete the following crossword puzzles, using the given hints.

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:

Question Image

Angles in the same segment of a circle are equal.

Important Questions on Geometry

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