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NCERT exemplar Class 9 Maths solutions chapter 8 deals with quadrilaterals and its properties. The NCERT exemplar Class 9 Maths chapter 8 solutions are prepared in such a way that students get an in-depth process flow to effectively approach the questions of NCERT Class 9 Maths. These NCERT exemplar Class 9 Maths chapter 8 solutions are curated by expert mathematicians at Careers360 and provide exhaustive solutions to the problems leading to a sturdy concept building of quadrilaterals. The NCERT exemplar Class 9 Maths solutions chapter 8 covers all the topics determined for CBSE Class 9 Syllabus.
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Question:1
If three angles of a quadrilateral are and then find the fourth angle
(A) 90^{o} (B)95^{o} (C) 105^{o} (D) 120^{o}
Question:2
A diagonal of a rectangle is inclined to one side of the rectangle at . The acute angle between the diagonals is
(A) 55^{0} (B) 50^{0} (C) 40^{0} (D)25^{0}
Question:3
ABCD is a rhombus such that . Then is
(A) 40^{0} (B) 45^{0} (C) 50^{0} (D)60^{0}
Question:4
The quadrilateral formed by joining the mid points of the sides of a quadrilateral PQRS taken in order is a rectangle. If
(A) PQRS is a rectangle
(B) PQRS is a parallelogram
(C) Diagonals of PQRS are perpendiculars
(D) Diagonals of PQRS are equal
Answer:
According to question quadrilateral, ABCD is formed by joining the midpoints of PQRSQuestion:5
(A) PQRS is a rhombus
(B) PQRS is a parallelogram
(C) diagonals of PQRS are perpendicular
(D) diagonals of PQRS are equal.
Answer:
According to question, the quadrilateral ABCD is formed by joining the midpoints of PQRSQuestion:6
If angles A, B, C and D of the quadrilateral ABCD, taken in order, are in the ratio 3:7:6:4, then ABCD is a
(A) rhombus (B) parallelogram
(C) trapezium (D) kite
Question:7
If bisectors of and of a quadrilateral ABCD intersect each other at P, of and at Q, of and at R and of and at S, then PQRS is a
(A) rectangle
(B) rhombus
(C) parallelogram
(D) quadrilateral whose opposite angles are supplementary
Question:8
, , and. If D and E are respectively the mid-points of AB and BC, determine the length of DE.
Answer:Question:9
Answer: TrueQuestion:8
If APB and CQD are two parallel lines, then the bisectors of the angles APQ, BPQ, CQP and PQD form
(A) a square (B) a rhombus
( C) a rectangle (D) any other parallelogram
Question:9
The figure obtained by joining the mid-points of the sides of a rhombus, taken in order, is:
(A) a rhombus (B) a rectangle
(C) a square (D) any parallelogram
Question:10
D and E are the mid-points of the sides AB and AC of DABC and O is any point on side BC. O is joined to A. If P and
Q are the mid-points of OB and OC respectively, then DEQP is
(A) a square (B) a rectangle
(C) a rhombus (D) a parallelogram
Question:11
The figure formed by joining the mid-points of the sides of a quadrilateral ABCD, taken in order, is a square only if,
(A) ABCD is a rhombus
(B) diagonals of ABCD are equal
(C) diagonals of ABCD are equal and perpendicular
(D) diagonals of ABCD are perpendicular.
Question:12
The diagonals AC and BD of a parallelogram ABCD intersect each other at thepoint O. If and , then is equal to
(A) (B) (C) (D)
Question:13
Which of the following is not true for a parallelogram?
(A) opposite sides are equal
(B) opposite angles are equal
(C) opposite angles are bisected by the diagonals
(D) diagonals bisect each other.
Question:14
D and E are the mid-points of the sides AB and AC respectively of . DE is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is
(A)
(B) AE = EF
(C) DE = EF
(D)
Question:1
Answer: 6 and 4Question:2
Answer: FalseQuestion:3
Can the angles and be the angles of a quadrilateral? Why or why Not? Explain
Answer: NoQuestion:4
In quadrilateral ABCD, .What special name can be given to this quadrilateral?
Answer: TrapeziumQuestion:5
All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?
Answer: Rectangle or SquareQuestion:6
Answer: FalseQuestion:7
Can all the four angles of a quadrilateral be obtuse angles? Give reason for your answer.
Answer: FalseQuestion:10
In Figure, ABCD and AEFG are two parallelograms. If , determine .
Answer:
Given: ABCD and AEFG are two parallelogramsQuestion:11
Can all the angles of a quadrilateral be acute angles? Give reason for your answer.
Answer: FalseQuestion:12
Can all the angles of a quadrilateral be right angles? Give reason for your answer.
Answer: YesQuestion:13
Diagonals of a quadrilateral ABCD bisect each other. If , determine .
Answer:
If the diagonals of a quadrilateral ABCD bisect each other then it parallelogram.
Sum of interior angles between two parallel lines is 180^{0} i.e.,
(given)
Question:14
Opposite angles of a quadrilateral ABCD are equal. If AB = 4 cm, determine CD.
Answer:Question:1
Answer:Question:2
ABCD is a trapezium in which and . Find angles C and D of the trapezium.
Answer:Question:
Answer:Question:4
ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the angles of the rhombus.
Answer:Question:5
Answer:
Given : ABCD is a parallelogram and AE = CFQuestion:6
Answer:
Given: ABCD is trapezium andQuestion:7
Answer:
Given : In , and and .Question:8
Answer:
Question:9
Answer:
Given: ABCD is a parallelogram and AP = CQQuestion:10
In Figure, P is the mid-point of side BC of a parallelogram ABCD such that . Prove that
.
Answer:
Given : ABCD is a parallelogram, P is a mid-point of BC such that .Question:1
Answer:
Given : Here ABC is an isosceles triangle and ADEF is a square inscribed in .Question:2
Answer: 4 cmQuestion:3
Answer:
Given : ABCD is a quadrilateral in which P, Q, R and S are the mid-points of sides AB, BC, CD and DA.Question:4
Answer:
Given: ABCD is a quadrilateral in which P, Q, R and S are the mid-points of sides AB, BC, CD and DA and . To prove: PQRS is a rectangleQuestion:5
Answer:
Given: ABCD is a parallelogram and P, Q, R and S are the mid-points of sides AB, BC, CD and AD. Also AC = BD and .Question:6
If a diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus.
Answer:
Let ABCD is a parallelogram and diagonal AC bisect the angle A andQuestion:7
Answer:
Given: ABCD is a parallelogram, P and Q are the mid-points of AB and CDQuestion:9
In Figure, , AB = DE, and AC = DF. Prove that and BC = EF.
Answer:
Given: andQuestion:10
E is the mid-point of a median AD of and BE is produced to meet AC at F. Show that .
Answer:
Given: In , AD is a median and E is the mid-point of ADQuestion:11
Answer:
Given: In a square ABCD; P, Q, R and S are the mid-points of AB, BC, CD and DA.Question:12
Answer:
Given: ABCD is a trapezium in which , E and F are the mid-points or sides AD and BC.Question:13
Answer:
Given: Let ABCD be a parallelogram and AP, BR, CQ, DS are the bisectors of
and respectively.Question:14
Answer:
Given: ABCD is a parallelogram whose diagonals bisect each other at O.Question:15
ABCD is a rectangle in which diagonal BD bisects . Show that ABCD is a square.
Answer:
Given: In a rectangle ABCD, diagonal BD bisects BQuestion:16
Answer:
Given: In , D, E and F are respectively the mid-points of the sides AB, BC and CA.Question:17
Answer:
Given: Let ABCD be a trapezium in which and let M and N be the mid-points of diagonals AC and BD.Question:18
Answer:
Given: In a parallelogram ABCD, P is the mid-point of DCThe chapter on Quadrilaterals in NCERT exemplar Class 9 Maths solutions chapter 8 covers the below-mentioned topics:
◊ Properties of angles within the quadrilateral and to prove that sum of all angles will be 360°.
◊ Sum of angles of any polygon of side length more than three.
◊ Different types of quadrilaterals such as rectangles, squares, parallelogram, trapezium, and rhombus.
◊ Condition for which any quadrilateral to be parallelogram trapezium rhombus et cetera.
◊ NCERT exemplar Class 9 Maths chapter 8 solutions discuss the midpoint theorem of the parallelogram, which will help us solve many geometry problems related to parallelograms.
These Class 9 Maths NCERT exemplar chapter 8 solutions give basic ideas of quadrilaterals and it is useful in higher classes. Students can use the Class 9 Maths NCERT exemplar solutions chapter 8 Quadrilaterals in the form of reference content to practice a variety of problems based on quadrilaterals. The detailed solutions are adequate for students to build a strong concept base and attempt books such as NCERT Class 9 Maths, RD Sharma Class 9 Maths, RS Aggarwal Class 9 Maths etcetera.
Chapter No. | Chapter Name |
Chapter 1 | |
Chapter 2 | |
Chapter 3 | |
Chapter 4 | |
Chapter 5 | |
Chapter 6 | |
Chapter 7 | |
Chapter 8 | |
Chapter 9 | |
Chapter 10 | |
Chapter 11 | |
Chapter 12 | |
Chapter 13 | |
Chapter 14 | |
Chapter 15 |
Yes, the rhombus is a special kind of parallelogram which diagonally intersects each other perpendicularly. All sides of the rhombus are equal, and the square is a special case of a rhombus.
The diamond in the playing card is the rhombus and sometimes rhombus is also called a diamond. We know that rhombus is a special case of parallelogram therefore diamond shape will be a parallelogram.
For any polygon of n sides, the sum of interior angle will be equal (n -2 )180°. For triangle n is equal to 3 hence the sum of interior angles will be 180°. For quadrilaterals n is equal to 4 hence the sum of interior angle will be 360°
NCERT exemplar Class 9 Maths solutions chapter 8 pdf download link enables the students to download/view the pdf version of the solutions in an offline environment.
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