651 + Interview Questions in GEOMETRY IN GENERAL AWARENESS Page 13 InterviewSolution

601.	Two parallel lines meet each other at some point.
Answer» The correct answer is False.

601.

Two parallel lines meet each other at some point.

Answer»

The correct answer is False.

Discussion

602.	Fill in the blanks to make the statements true:In Fig., points A, B, C, D and E are collinear such that AB = BC = CD = DE. Then(a) AD = AB + ______(b) AD = AC + ______(c) mid point of AE is ______(d) mid point of CE is ______(e) AE = ______ × AB.
Answer» (a) AD = AB + BD Where, BD = BC + CD (b) AD = AC + CD (c) mid point of AE is c (d) mid point of CE is D (e) AE = 4 × AB. [given]

602.

Fill in the blanks to make the statements true:In Fig., points A, B, C, D and E are collinear such that AB = BC = CD = DE. Then(a) AD = AB + (b) AD = AC + (c) mid point of AE is (d) mid point of CE is (e) AE = __ × AB.

Answer»

(a) AD = AB + BD

Where, BD = BC + CD

(b) AD = AC + CD

(c) mid point of AE is c

(d) mid point of CE is D

(e) AE = 4 × AB. [given]

Discussion

603.	Fill in the blank,In Fig. 9.1, the line segments PQ and RQ have been marked on a line l such that PQ = AB and RQ = CD. Then AB – CD =__________.
Answer» Then AB – CD = PR

Discussion

604.	In the following figure, PQ is parallel to BC and `PQ:BC =1 :3`. If the area of the triangle ABC is `144 cm^2`, then what is the area of the triangle APQ? A. `48 cm ^2`B. `36cm ^2`C. `16 cm ^2`D. `9cm^2`
Answer» Correct Answer - C The ratio of areas of two similar triangles equal to the ratio of the squares of their corresponding sides.

Discussion

605.	A cyclic polygon has n sides such that each of its interior angle measures `144^(@)`. What is the measures of the angle subtended by each of its side at the geometrical center of the polygon.A. `144^(@)`B. `30^(@)`C. `36^(@)`D. `54^(@)`
Answer» Correct Answer - C Find the number of sides of the polygon, anlge subtended at the center `=360^(@)/n`.

Discussion

606.	In `DeltaPQR and Delta ABC`, `angleQ=angleB=90^(@),PQ=AB, and QR=BC`. Which of the following property can be used to prove the congruence of `DeltaPQR` and `DeltaABC` ?A. SSSB. RHSC. ASAD. SAS
Answer» Correct Answer - D Given `PQ=AB, QR=BC, angle Q=angleB=90^(@)`. Basically by using SAS congruence property. ` DeltaPQR~=ABC`. Hence, the correct option is (d).

Discussion

607.	In two triangles ABC an DEF,`angle A=angleD`. The sum of the angles A and B is equal to the sum of the angles D and E. If `BC=6` cm and `EF=8cm`, find the ratio of the areas of the triangles, ABC and DEF.A. `3:4 `B. `4:3`C. `9:16`D. `16:9`
Answer» Correct Answer - C The ratio of areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

Discussion

608.	A man travels on a bicycle, 10 km east from the starting point A to reach point B, then the cycles 15 km south to reach point C. Find the shortest distance between A and C.A. 25 kmB. 5kmC. `25sqrt(13) km`D. `5sqrt(13) km`
Answer» Correct Answer - D Apply Pythagoras theorem.

Discussion

609.	In the following figure, PQ is parallel to BC and `PQ:BC =1 :3`. If the area of the triangle ABC is `144 cm^2`, then what is the area of the triangle APQ? A. `48 cm ^2`B. `36cm ^2`C. `16 cm ^2`D. `9cm^2`
Answer» Correct Answer - C The ratio of areas of two similar triangles equal to the ratio of the squares of their corresponding sides.

Discussion

610.	In triangle ABC , sides AB and AC are extended to D and E, respectively, such that `AB=BD` and AC =CE`, Find DE, if `BC=6 cm`.A. 3 cmB. 6cmC. 9 cmD. 12 cm
Answer» Correct Answer - C Apply basic proportionality theorem.

Discussion

611.	Using the information given, name the right angles in each part of Fig.is RS⊥RW?
Answer» The correct answer is ∠RTW and ∠RTS

611.

Using the information given, name the right angles in each part of Fig.is RS⊥RW?

Answer»

The correct answer is ∠RTW and ∠RTS

Discussion

612.	Using the information given, name the right angles in each part of Fig.AC⊥ CD?
Answer» The correct answer is ∠ACD.

612.

Using the information given, name the right angles in each part of Fig.AC⊥ CD?

Answer»

The correct answer is ∠ACD.

Discussion

613.	Using the information given, name the right angles in each part of Fig.AE⊥ CE?
Answer» The correct answer is ∠AEC.

Discussion

614.	In Fig., ∠BAC = 90° and AD ⊥ BC. The number of right triangles in the figure is(A) 1 (B) 2 (C) 3 (D) 4
Answer» (C) 3 We have, ∠BAC = 90° and AD ⊥ BC ∵ ∠BDA = ∠CDA = ∠BAC = 90° ∴ There are 3 right triangles formed in the given figure.

614.

In Fig., ∠BAC = 90° and AD ⊥ BC. The number of right triangles in the figure is(A) 1 (B) 2 (C) 3 (D) 4

Answer»

(C) 3

We have, ∠BAC = 90° and AD ⊥ BC

∵ ∠BDA = ∠CDA = ∠BAC = 90°

∴ There are 3 right triangles formed in the given figure.

Discussion

615.	A polygon has prime number of sides. Its number of sides is equal to the sum of the two least consecutive primes. The number of diagonals of the polygon is(A) 4 (B) 5 (C) 7 (D) 10
Answer» (B) 5 The two least consecutive prime numbers are, 2 and 3 Sum of two numbers = 2 + 3 = 5 By using formula = n(n – 3)/2 = 5(5 – 3)/2 = (5 × 2)/2 = 10/2 = 5

615.

A polygon has prime number of sides. Its number of sides is equal to the sum of the two least consecutive primes. The number of diagonals of the polygon is(A) 4 (B) 5 (C) 7 (D) 10

Answer»

(B) 5

The two least consecutive prime numbers are, 2 and 3

Sum of two numbers = 2 + 3 = 5

By using formula = n(n – 3)/2

= 5(5 – 3)/2

= (5 × 2)/2

= 10/2

= 5

Discussion

616.	Using the information given, name the right angles in each part of Fig.AC⊥ BD?
Answer» The correct answer is ∠AED,∠AEB,∠BEC and ∠DEC.

Discussion

617.	Using the information given, name the right angles in each part of Fig.is AC⊥ BD?
Answer» The correct answer is ∠ACD and ∠ACB

617.

Using the information given, name the right angles in each part of Fig.is AC⊥ BD?

Answer»

The correct answer is ∠ACD and ∠ACB

Discussion

618.	In Fig., AB = BC and AD = BD = DC. The number of isosceles triangles in the figure is(A) 1 (B) 2 (C) 3 (D) 4
Answer» (C) 3 ∵ We have, AB = BC and AD = BD = DC. ∴ ∆ ABD, ∆ BDC and ∆ ABC all are isosceles triangles. ∴ There are 3 isosceles triangles formed in the given figure.

618.

In Fig., AB = BC and AD = BD = DC. The number of isosceles triangles in the figure is(A) 1 (B) 2 (C) 3 (D) 4

Answer»

(C) 3

∵ We have, AB = BC and AD = BD = DC.

∴ ∆ ABD, ∆ BDC and ∆ ABC all are isosceles triangles.

∴ There are 3 isosceles triangles formed in the given figure.

Discussion

619.	In Fig, if AC ⊥ BD , then name all the right angles.
Answer» There are four right angles. They are: ∠APD , ∠APB, ∠BPC and ∠CPD.

619.

In Fig, if AC ⊥ BD , then name all the right angles.

Answer»

There are four right angles.

They are: ∠APD , ∠APB, ∠BPC and ∠CPD.

Discussion

620.	Find out the incorrect statement, if any, in the following: An angle is formed when we have (a) two rays with a common end-point (b) two line segments with a common end-point (c) a ray and a line segment with a common end-point
Answer» The correct answer is (b) and (c)

620.

Find out the incorrect statement, if any, in the following: An angle is formed when we have (a) two rays with a common end-point (b) two line segments with a common end-point (c) a ray and a line segment with a common end-point

Answer»

The correct answer is (b) and (c)

Discussion

621.	In Fig, PQ ⊥ AB and PO = OQ. Is PQ the perpendicular bisector of line segment AB? Why or why not?
Answer» PQ is not the perpendicular bisector of line segment AB, because AO ≠ BO. [Note: AB is the perpendicular bisector of line segment PQ].

Discussion

622.	In Fig. 2.1, PQ ⊥ AB and PO = OQ. Is PQ the perpendicular bisector of line segment AB? Why or why not?
Answer» PQ is not the perpendicular bisector of line segment AB, because AO ≠ BO. [Note: AB is the perpendicular bisector of line segment PQ]. PQ is not the perpendicular bisector of line segment AB, because AO ≠ BO. [Note: AB is the perpendicular bisector of line segment PQ].

Discussion

623.	If line PQ \|\| line m, then line segment PQ \|\| m
Answer» The correct answer is True.

623.

If line PQ || line m, then line segment PQ || m

Answer»

The correct answer is True.

Discussion

624.	The number of independent measurement required to construct an isosceles trapezium is three.
Answer» Correct Answer - True

Discussion

625.	Number of independent measurement required to construct a triangle is ______
Answer» Correct Answer - 3

Discussion

626.	Construct a parallelogram PQRS, when `PQ=3.7 cm, QR=2.3cm, and PR=4.8cm`.
Answer» Steps: 1. Draw a line segment PQ=3.7 cm. 2. Draw an arc with P as the centre and a radius of 4.8 cm. 3. With Q as the centre and a radius of 2.3 cm, draw another arc to intersect the previous are of step 2 at R and join QR. 4. With R as the centre , draw an arc of radius 3.7 cm. 5. With P as the centre, draw another arc of radius 2.3 cm to intersect the arc in step 4 at S. Join RS and PS. PQRS is the required parallelogram.

Discussion

627.	In Fig. 2.39, (a) What is AE + EC? (b) What is AC – EC? (c) What is BD – BE? (d) What is BD – DE?
Answer» (a) AC (b) AE (c) ED (d) BE

627.

In Fig. 2.39, (a) What is AE + EC? (b) What is AC – EC? (c) What is BD – BE? (d) What is BD – DE?

Answer»

(a) AC (b) AE (c) ED (d) BE

Discussion

628.	In the adjoining figure, O is the centre of the circle. AB is an arc of the circle and `/_AOB=80^(@)`. Find `/_ACB`.
Answer» The angle made by an arc at the centre of a circle is twice the angle made by the arc point on the remaining part of the circle. `/_AOB=2 /_ACB` `implies 2 /_ACB=80^(@)` `implies /_ACB =40^(@)`

Discussion

629.	The number of independent measurement required to construct a circle is two.
Answer» Correct Answer - False

Discussion

630.	Centroid of a triangle divides its median in the ratio of 1:2 from the vertex.
Answer» Correct Answer - False

Discussion

631.	Find out the incorrect statement, if any, in the following: An angle is formed when we have (a) two rays with a common end-point (b) two line segments with a common end-point (c) a ray and a line segment with a common end-point
Answer» All the three statements (a), (b) and (c) are incorrect. ∵ The common initial point of two rays forms an angle.

631.

Find out the incorrect statement, if any, in the following: An angle is formed when we have (a) two rays with a common end-point (b) two line segments with a common end-point (c) a ray and a line segment with a common end-point

Answer»

All the three statements (a), (b) and (c) are incorrect.

∵ The common initial point of two rays forms an angle.

Discussion

632.	The point of concurrence of altitudes of a triangle is called orthocentre.
Answer» Correct Answer - True

Discussion

633.	In which of the following figures,(a) perpendicular bisector is shown?(b) bisector is shown?(c) only bisector is shown?(d) only perpendicular is shown?
Answer» (a) Figure (ii) shows the perpendicular bisector (b) Figure (ii) and (iii) shows the bisector. (c) Figure (iii) shows only the bisector. (d) Figure (i) shows only the perpendicular.

633.

In which of the following figures,(a) perpendicular bisector is shown?(b) bisector is shown?(c) only bisector is shown?(d) only perpendicular is shown?

Answer»

(a) Figure (ii) shows the perpendicular bisector

(b) Figure (ii) and (iii) shows the bisector.

(c) Figure (iii) shows only the bisector.

(d) Figure (i) shows only the perpendicular.

Discussion

634.	The point of concurrence of medians of a triangle is called centroid.
Answer» Correct Answer - True

Discussion

635.	The image of a point lying on a line l with respect to the line of symmetry l lies on _______.
Answer» The image of a point lying on a line l with respect to the line of symmetry l lies on ɭ

Discussion

636.	Given below are some figures. Choose the image of the given figure with respect to the given line from the given choices. A. B. C. D.
Answer» Correct Answer - a

Discussion

637.	What is common in the following figures (i) and (ii)?Is figure (i) that of triangle ? if not, why?
Answer» Both the figures (i) and (ii) have 3 line segments. No, Fig. (i) is not a triangle since the three line segments does not form a closed figure.

Discussion

638.	If two rays intersect, will their point of intersection be the vertex of an angle of which the rays are the two sides?
Answer» Yes If two rays intersect, will their point of intersection be the vertex of an angle of which the rays are the two sides.

638.

If two rays intersect, will their point of intersection be the vertex of an angle of which the rays are the two sides?

Answer»

Yes

If two rays intersect, will their point of intersection be the vertex of an angle of which the rays are the two sides.

Discussion

639.	In given figure,(a) is AC + CB = AB ?(b) is AB + AC= CB ?(c) is AB + BC = CA ?
Answer» (a) Yes, AC + CB = AB (b) No, AB – AC = CB (c) No, AB – BC = CA

639.

In given figure,(a) is AC + CB = AB ?(b) is AB + AC= CB ?(c) is AB + BC = CA ?

Answer»

(a) Yes, AC + CB = AB

(b) No, AB – AC = CB

(c) No, AB – BC = CA

Discussion

640.	In Fig. 2.38, (a) is AC + CB = AB? (b) is AB + AC = CB? (c) is AB + BC = CA?
Answer» (a) Yes (b) No (c) No .

640.

In Fig. 2.38, (a) is AC + CB = AB? (b) is AB + AC = CB? (c) is AB + BC = CA?

Answer»

(a) Yes (b) No (c) No

.

Discussion

641.	In given figure,(a) name any four angles that appear to be acute angles.(b) name any two angles that appear to be obtuse angles.
Answer» (a) Acute angles : ∠ADE, ∠AEB, ∠ABE and ∠ECD. (b) Obtuse angles : ∠BCD and ∠BAD.

641.

In given figure,(a) name any four angles that appear to be acute angles.(b) name any two angles that appear to be obtuse angles.

Answer»

(a) Acute angles : ∠ADE, ∠AEB, ∠ABE and ∠ECD.

(b) Obtuse angles : ∠BCD and ∠BAD.

Discussion

642.	In the following, CDEF is a cyclic quadrilateral. `bar(CG)` and `bar(DH)` are the angle bisectors of `angleC` and `angleD` respectively. If `angleE=100^(@)` and `angleF=110^(@)`, then find `angleCPD`.
Answer» In a cyclic quadrilateral, opposite angles are supplementary.

Discussion

643.	The angle subtended by a minor arc in its alternate segment is…………….A. acuteB. obtuseC. `90^(@)`D. reflex angle.
Answer» Correct Answer - A Angle subtended by a minor arc is always less than `90^(@)`.

Discussion

644.	A tower of height 60 m casts a 40 m long shadow on the ground. At the same time, a needle of height 12 m casts a `x` cm long shadow the ground. Find `x`A. 6B. 8C. 10D. 14
Answer» Correct Answer - B Join,BD, ABDE is a cyclic quadrilateral.

Discussion

645.	A pole of height 14 m casts a 10 m long shadow on the ground. At the same time, a tower casts a 70 m long shadow on the ground. Find the height of the tower.A. 50 mB. 78 mC. 90 mD. 98 m
Answer» Correct Answer - D Use the concept of similar triangles.

Discussion

646.	Find the distance between the helicopter and the ship.
Answer» From the figure AS is the distance between the helicopter and the ship. ∆ APS is a right angled triangle, by Pythagoras theorem, AS² = AP² + PS² = 80² + 150² = 6400 + 22500 = 28900 = 170² ∴ The distance between the helicopter and the ship is 170 m

646.

Find the distance between the helicopter and the ship.

Answer»

From the figure AS is the distance between the helicopter and the ship.

∆ APS is a right angled triangle, by Pythagoras theorem,

AS² = AP² + PS²

= 80² + 150²

= 6400 + 22500 = 28900 = 170²

∴ The distance between the helicopter and the ship is 170 m

Discussion

647.	How many edges, faces and vertices are there in a sphere?
Answer» No edges, No faces and No vertices.

Discussion

648.	ABCD is a rhombus, in which the length of the diagonals AC and BD are 6 cm and 8cm, respectively. Find the perimeter of the rhombus ABCD.
Answer» Correct Answer - 20 cm

Discussion

649.	In a parallelogram PQRS, the bisectors of `/_P` and `/_Q` meet on RS.If the perimeter PQRS is 13.5 cm, then find the measure of QRA. 4.5 cmB. 2.25 cmC. 3 cmD. 3.75cm
Answer» Correct Answer - b

Discussion

650.	If the three angles of a triangle are in the ratio 3 : 5 : 4, then find them.
Answer» Given three angles of the triangles are in the ratio 3 : 5 : 4. Let the three angle be 3x, 5x and 4x. By angle sum property of a triangle, we have 3x + 5x + 4x = 180° 12x = 180° x = \(\frac{180°}{12}\) x = 15° ∴ The angle are 3x = 3 x 15° = 45° 5x = 5 x 15° = 75° 4x = 4 x 15° = 60° Three angles of the triangle are 45°, 75°, 60°

650.

If the three angles of a triangle are in the ratio 3 : 5 : 4, then find them.

Answer»

Given three angles of the triangles are in the ratio 3 : 5 : 4.

Let the three angle be 3x, 5x and 4x.

By angle sum property of a triangle, we have

3x + 5x + 4x = 180°

12x = 180°

x = \(\frac{180°}{12}\)

x = 15°

∴ The angle are 3x = 3 x 15°

= 45°

5x = 5 x 15°

= 75°

4x = 4 x 15°

= 60°

Three angles of the triangle are 45°, 75°, 60°

Discussion

Explore topic-wise InterviewSolutions in .

Two parallel lines meet each other at some point.

Fill in the blanks to make the statements true:In Fig., points A, B, C, D and E are collinear such that AB = BC = CD = DE. Then(a) AD = AB + ______(b) AD = AC + ______(c) mid point of AE is ______(d) mid point of CE is ______(e) AE = ______ × AB.

Fill in the blank,In Fig. 9.1, the line segments PQ and RQ have been marked on a line l such that PQ = AB and RQ = CD. Then AB – CD =__________.

In the following figure, PQ is parallel to BC and `PQ:BC =1 :3`. If the area of the triangle ABC is `144 cm^2`, then what is the area of the triangle APQ? A. `48 cm ^2`B. `36cm ^2`C. `16 cm ^2`D. `9cm^2`

A cyclic polygon has n sides such that each of its interior angle measures `144^(@)`. What is the measures of the angle subtended by each of its side at the geometrical center of the polygon.A. `144^(@)`B. `30^(@)`C. `36^(@)`D. `54^(@)`

In `DeltaPQR and Delta ABC`, `angleQ=angleB=90^(@),PQ=AB, and QR=BC`. Which of the following property can be used to prove the congruence of `DeltaPQR` and `DeltaABC` ?A. SSSB. RHSC. ASAD. SAS

In two triangles ABC an DEF,`angle A=angleD`. The sum of the angles A and B is equal to the sum of the angles D and E. If `BC=6` cm and `EF=8cm`, find the ratio of the areas of the triangles, ABC and DEF.A. `3:4 `B. `4:3`C. `9:16`D. `16:9`

A man travels on a bicycle, 10 km east from the starting point A to reach point B, then the cycles 15 km south to reach point C. Find the shortest distance between A and C.A. 25 kmB. 5kmC. `25sqrt(13) km`D. `5sqrt(13) km`

In the following figure, PQ is parallel to BC and `PQ:BC =1 :3`. If the area of the triangle ABC is `144 cm^2`, then what is the area of the triangle APQ? A. `48 cm ^2`B. `36cm ^2`C. `16 cm ^2`D. `9cm^2`

In triangle ABC , sides AB and AC are extended to D and E, respectively, such that `AB=BD` and AC =CE`, Find DE, if `BC=6 cm`.A. 3 cmB. 6cmC. 9 cmD. 12 cm

Using the information given, name the right angles in each part of Fig.is RS⊥RW?

Using the information given, name the right angles in each part of Fig.AC⊥ CD?

Using the information given, name the right angles in each part of Fig.AE⊥ CE?

In Fig., ∠BAC = 90° and AD ⊥ BC. The number of right triangles in the figure is(A) 1 (B) 2 (C) 3 (D) 4

A polygon has prime number of sides. Its number of sides is equal to the sum of the two least consecutive primes. The number of diagonals of the polygon is(A) 4 (B) 5 (C) 7 (D) 10

Using the information given, name the right angles in each part of Fig.AC⊥ BD?

Using the information given, name the right angles in each part of Fig.is AC⊥ BD?

In Fig., AB = BC and AD = BD = DC. The number of isosceles triangles in the figure is(A) 1 (B) 2 (C) 3 (D) 4

In Fig, if AC ⊥ BD , then name all the right angles.

Find out the incorrect statement, if any, in the following: An angle is formed when we have (a) two rays with a common end-point (b) two line segments with a common end-point (c) a ray and a line segment with a common end-point

In Fig, PQ ⊥ AB and PO = OQ. Is PQ the perpendicular bisector of line segment AB? Why or why not?

In Fig. 2.1, PQ ⊥ AB and PO = OQ. Is PQ the perpendicular bisector of line segment AB? Why or why not?

If line PQ || line m, then line segment PQ || m

The number of independent measurement required to construct an isosceles trapezium is three.

Number of independent measurement required to construct a triangle is ______

Construct a parallelogram PQRS, when `PQ=3.7 cm, QR=2.3cm, and PR=4.8cm`.

In Fig. 2.39, (a) What is AE + EC? (b) What is AC – EC? (c) What is BD – BE? (d) What is BD – DE?

In the adjoining figure, O is the centre of the circle. AB is an arc of the circle and `/_AOB=80^(@)`. Find `/_ACB`.

The number of independent measurement required to construct a circle is two.

Centroid of a triangle divides its median in the ratio of 1:2 from the vertex.

Find out the incorrect statement, if any, in the following: An angle is formed when we have (a) two rays with a common end-point (b) two line segments with a common end-point (c) a ray and a line segment with a common end-point

The point of concurrence of altitudes of a triangle is called orthocentre.

In which of the following figures,(a) perpendicular bisector is shown?(b) bisector is shown?(c) only bisector is shown?(d) only perpendicular is shown?

The point of concurrence of medians of a triangle is called centroid.

The image of a point lying on a line l with respect to the line of symmetry l lies on _______.

Given below are some figures. Choose the image of the given figure with respect to the given line from the given choices. A. B. C. D.

What is common in the following figures (i) and (ii)?Is figure (i) that of triangle ? if not, why?

If two rays intersect, will their point of intersection be the vertex of an angle of which the rays are the two sides?

In given figure,(a) is AC + CB = AB ?(b) is AB + AC= CB ?(c) is AB + BC = CA ?

In Fig. 2.38, (a) is AC + CB = AB? (b) is AB + AC = CB? (c) is AB + BC = CA?

In given figure,(a) name any four angles that appear to be acute angles.(b) name any two angles that appear to be obtuse angles.

In the following, CDEF is a cyclic quadrilateral. `bar(CG)` and `bar(DH)` are the angle bisectors of `angleC` and `angleD` respectively. If `angleE=100^(@)` and `angleF=110^(@)`, then find `angleCPD`.

The angle subtended by a minor arc in its alternate segment is…………….A. acuteB. obtuseC. `90^(@)`D. reflex angle.

A tower of height 60 m casts a 40 m long shadow on the ground. At the same time, a needle of height 12 m casts a `x` cm long shadow the ground. Find `x`A. 6B. 8C. 10D. 14

A pole of height 14 m casts a 10 m long shadow on the ground. At the same time, a tower casts a 70 m long shadow on the ground. Find the height of the tower.A. 50 mB. 78 mC. 90 mD. 98 m

Find the distance between the helicopter and the ship.

How many edges, faces and vertices are there in a sphere?

ABCD is a rhombus, in which the length of the diagonals AC and BD are 6 cm and 8cm, respectively. Find the perimeter of the rhombus ABCD.

In a parallelogram PQRS, the bisectors of `/_P` and `/_Q` meet on RS.If the perimeter PQRS is 13.5 cm, then find the measure of QRA. 4.5 cmB. 2.25 cmC. 3 cmD. 3.75cm

If the three angles of a triangle are in the ratio 3 : 5 : 4, then find them.

Fill in the blanks to make the statements true:In Fig., points A, B, C, D and E are collinear such that AB = BC = CD = DE. Then(a) AD = AB + (b) AD = AC + (c) mid point of AE is (d) mid point of CE is (e) AE = __ × AB.