Maharashtra Board for Class 8, Maths Chapter 17

Class 8: Maths Chapter 17 solutions. Complete Class 8 Maths Chapter 17 Notes.

Contents

1 Maharashtra Board Solutions Class 8-Maths (Practice Set 17.2): Chapter 17- Factorisation of Algebraic Expressions
2 Download PDF
3 Chapterwise Maharashtra Board Solutions Class 8 Maths :
4 FAQs
5 About Maharashtra State Board (MSBSHSE)

Maharashtra Board Solutions Class 8-Maths (Practice Set 17.2): Chapter 17- Factorisation of Algebraic Expressions

Maharashtra Board 8th Maths Chapter 17, Class 8 Maths Chapter 17 solutions

Question 1.
The diameters PQ and RS of the circle with centre C are perpendicular to each other at C. State, why arc PS and arc SQ are congruent. Write the other arcs which are congruent to arc PS.

Solution:
diameter PQ ⊥ diameter RS … [Given]
∴ m∠PCS = m∠SCQ = m∠PCR = m∠RCQ = 90°
The measure of the angle subtended at the centre by an arc is the measure of the arc.
∴ m(arc PS) = m∠PCS = 90° …(i)
m (arc SQ) = m∠SCQ = 90° …(ii)
∴ m(arc PS) = m(arc SQ) … [From (i) and (ii)]
∴ arc PS ≅ arc SQ … [If the measures of two arcs of a circle are same, then the two arcs are congruent]
m(arc PR) = m∠PCR = 90° .. .(iii)
m (arc RQ) = m∠RCQ = 90° … (iv)
∴ m(arc PS) = m(arc PR) = m(arc RQ) … [From (i), (iii) and (iv)]
∴ arc PS ≅ arc PR ≅ arc RQ
… [If the measures of two arcs of a circle are same, then the two arcs are congruent]
∴ arc PR and arc RQ are congruent to arc PS.

Question 2.
In the given figure, O is the centre of the circle whose diameter is MN. Measures of some central angles are given in the figure.
i. m∠AOB and m∠COD
ii. Show that arc AB ≅ arc CD
iii. Show that chord AB ≅ chord CD

Solution:
i. Seg MN is the diameter of the circle. … [Given]
∴ m∠AOM + m∠AON = 180° … [Angles in a linear pair]
∴ m∠AOM + (m∠AOB + m∠BON) = 180° … [Angle addition property]
∴ 100° + m∠AOB + 35° = 180°
…[∵ m∠AOM = 100°, m∠BON = 35°]
∴ m∠AOB + 135° = 180°
∴ m∠AOB = 180°- 135°
∴m∠AOB = 45° …(i)
Also, m∠DOM + m∠DON = 180° … [Angles in a linear pair]
∴ m∠DOM + (m∠COD + m∠CON) = 180° … [Angle addition property]
∴ 100° +m∠COD + 35°= 180°
…[∵ m∠DOM = 100°, m∠CON = 35° ]
∴ m∠COD + 135° = 180°
∴ m∠COD = 180°- 135°
∴ m∠COD = 45° …(ii)

ii. m(arc AB) = m∠AOB = 45° … [From (i)]
m(arc DC) = m∠DOC = 45° .. .[From (ii)]
∴ m(arc AB) = m(arc DC) …[From (i) and (ii)]
∴ arc AB ≅ arc CD
… [If the measures of two arcs of a circle are same, then the two arcs are congruent]

iii. arc AB ≅ arc CD
∴ chord AB ≅ chord CD ….[The chords corresponding to congruent arcs are congruent]

Intext Questions and Activities

Question 1.
If the measures of two arcs of a circle are same, then two arcs are congruent. Verify this property using tracing paper. (Textbook pg. no. 117)
Solution:
[Students should attempt the above activities on their own.]

Question 2.
With the help of following activity find out the properties of the chord and the corresponding arc.
i. a. Draw a circle with centre O.
b. Draw ∠COD and ∠AOB of same measure.
You will find that the arc AXB and arc CYD are congruent.
c. Draw chords AB and CD.
d. Using compass experience that the length of chord AB and chord CD is also same.
(Textbook pg. no. 117)

Solution:
[Students should attempt the above activities on their own.]

ii. a. Draw a circle with centre C.
b. Draw the congruent chords AB and DE of the circle. Draw the radii CA, CB, CD and CE.
c. Check that ∠ACB and ∠DCE are congruent.
d. Hence show that measure of arc AB and arc DE is equal. Hence these arcs are congruent. (Textbook pg. no. 117)

Solution:
[Students should attempt the above activities on their own.]

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Maharashtra Board Solutions Class 8-Maths (Practice Set 17.2): Chapter 17- Factorisation of Algebraic Expressions

Download PDF: Maharashtra Board Solutions Class 8-Maths (Practice Set 17.2): Chapter 17- Factorisation of Algebraic Expressions PDF

Chapterwise Maharashtra Board Solutions Class 8 Maths :

FAQs

Where do I get the Maharashtra State Board Books PDF For free download?

You can download the Maharashtra State Board Books from the eBalbharti official website, i.e. cart.ebalbharati.in or from this article.

How to Download Maharashtra State Board Books?

Students can get the Maharashtra Books for primary, secondary, and senior secondary classes from here. You can view or download the Maharashtra State Board Books from this page or from the official website for free of cost. Students can follow the detailed steps below to visit the official website and download the e-books for all subjects or a specific subject in different mediums.
Step 1: Visit the official website ebalbharati.in
Step 2: On the top of the screen, select “Download PDF textbooks”
Step 3: From the “Classes” section, select your class.
Step 4: From “Medium”, select the medium suitable to you.
Step 5: All Maharashtra board books for your class will now be displayed on the right side.
Step 6: Click on the “Download” option to download the PDF book.

Who developed the Maharashtra State board books?

As of now, the MSCERT and Balbharti are responsible for the syllabus and textbooks of Classes 1 to 8, while Classes 9 and 10 are under the Maharashtra State Board of Secondary and Higher Secondary Education (MSBSHSE).

How many state boards are there in Maharashtra?

The Maharashtra State Board of Secondary & Higher Secondary Education, conducts the HSC and SSC Examinations in the state of Maharashtra through its nine Divisional Boards located at Pune, Mumbai, Aurangabad, Nasik, Kolhapur, Amravati, Latur, Nagpur and Ratnagiri.

About Maharashtra State Board (MSBSHSE)

The Maharashtra State Board of Secondary and Higher Secondary Education or MSBSHSE (Marathi: महाराष्ट्र राज्य माध्यमिक आणि उच्च माध्यमिक शिक्षण मंडळ), is an autonomous and statutory body established in 1965. The board was amended in the year 1977 under the provisions of the Maharashtra Act No. 41 of 1965.

The Maharashtra State Board of Secondary & Higher Secondary Education (MSBSHSE), Pune is an independent body of the Maharashtra Government. There are more than 1.4 million students that appear in the examination every year. The Maha State Board conducts the board examination twice a year. This board conducts the examination for SSC and HSC.

The Maharashtra government established the Maharashtra State Bureau of Textbook Production and Curriculum Research, also commonly referred to as Ebalbharati, in 1967 to take up the responsibility of providing quality textbooks to students from all classes studying under the Maharashtra State Board. MSBHSE prepares and updates the curriculum to provide holistic development for students. It is designed to tackle the difficulty in understanding the concepts with simple language with simple illustrations. Every year around 10 lakh students are enrolled in schools that are affiliated with the Maharashtra State Board.