{"id":623881,"date":"2023-08-31T12:50:00","date_gmt":"2023-08-31T12:50:00","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=623881"},"modified":"2023-08-31T12:50:19","modified_gmt":"2023-08-31T12:50:19","slug":"kc-sinha-exercise-10-1-mathematics-solution-class-9-chapter-10-quadrilaterals","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-10-1-mathematics-solution-class-9-chapter-10-quadrilaterals\/","title":{"rendered":"KC Sinha: Exercise 10.1 – Mathematics Solution Class 9 Chapter 10 Quadrilaterals"},"content":{"rendered":"\n\n\n\n\n

EXERCISE 10.1<\/h3>\n\n\n\n
\n\n\n\n

Type 1<\/strong><\/p>\n\n\n\n

\n\n\n\n

QUESTION 1<\/h4>\n\n\n\n

Fill in the blanks:
(i) A parallelogram will be a rhombus, if and only if its ___are Perpendicular to each other.
(ii) A quadrilateral will be a parallelogram, if and only if its diagonals ___ each other.
(iii) Opposite angles of a parallelogram are __
Sol :<\/p>\n\n\n\n

\n\n\n\n

QUESTION 2<\/h4>\n\n\n\n

Which of the following statements are true (T) and which are false (F)
(i) In any quadrilateral, if a pair or opposite is equal, it is a parallelogram.
(ii) In a parallelogram , diagonals bisect each other.
(iii) If all sides of a quadrilateral are equal, it is a parallelogram.
(iv) In a quadrilateral, if three angles are equal, it is a parallelogram.<\/p>\n\n\n\n

(v) In a quadrilateral , if its opposite sides are of equal lengths , it is a parallelogram .
Sol :<\/p>\n\n\n\n

\n\n\n\n

QUESTION 3<\/h4>\n\n\n\n

Answer the following questions :
(i) What is the relation between the diagonals of a rhombus ?
(ii) For a parallelogram to be square , what will be the relation between its diagonals ?
Sol :<\/p>\n\n\n\n

\n\n\n\n

QUESTION 4<\/h4>\n\n\n\n

(i) In a parallelogram ABCD, if \u2220D=110\u00b0 , then write the measure in degree of \u2220A and \u2220B
(ii) In a parallelogram, sum of two angles is 140\u00b0 , then find the measure of its acute angle.<\/p>\n\n\n\n

(iii) In a parallelogram, one angle is 4\/5 of its adjacent angle , then find the values of both the adjacent angles in degree.
(iv) Side BC of a parallelogram is produced to point E. If \u2220DCE=65\u00b0, find the value of \u2220A.
Sol :<\/p>\n\n\n\n

\n\n\n\n

QUESTION 5<\/h4>\n\n\n\n

In a parallelogram ABCD , \u2220DAC=40\u00b0 ,\u2220ABC=60\u00b0 , then fill in the blanks .
(a) \u2220ACB__
(b) \u2220ADC__
(c) \u2220BAC__
(d) \u2220ACD__
Sol :<\/p>\n\n\n\n

\n\n\n\n

QUESTION 6<\/h4>\n\n\n\n

ABCD is a rhombus whose diagonals meet at a point O , if \u2220OAB=30\u00b0 , then find \u2220OBA<\/strong>
Sol :<\/p>\n\n\n\n

\n\n\n\n

QUESTION 7<\/h4>\n\n\n\n

ABCD is a parallelogram whose diagonals AC and BD intersect each other at point O , such that \u2220DAC=32\u00b0 and \u2220AOB=70\u00b0 , find the value of \u2220DBC.<\/strong>
Sol :<\/p>\n\n\n\n

\n\n\n\n

QUESTION 8<\/h4>\n\n\n\n

In the adjacent figure , ABCD is a parallelogram in which \u2220DAO=35\u00b0 , \u2220OAB=25\u00b0 , \u2220DOC=75\u00b0 , find
\"\"
(i) \u2220ABO
(ii) \u2220ODC
(iii) \u2220ACB
(iv) \u2220CBD
Sol :<\/p>\n\n\n\n

\n\n\n\n

QUESTION 9<\/h4>\n\n\n\n

In a rhombus, lengths of diagonals are 8 cm and 6 cm. f\u200cind the length of its sides<\/strong>
Sol :<\/p>\n\n\n\n

\n\n\n\n

QUESTION 10<\/h4>\n\n\n\n

In a rhombus, length of a side and one diagonal are 13 cm and 10 cm respectively. Find the length of its other diagonal.<\/strong>
Sol :<\/p>\n\n\n\n

\n\n\n\n

QUESTION 11<\/h4>\n\n\n\n

In the adjacent figure, PQ||SR and PS=PR , find \u03b1 and \u03b2<\/strong>
\"In
Sol :
[Hint : PS=PR
\u2220PSR=\u2220PRS=\u03b1
In \u0394PSR \u03b1+\u03b1+30\u00b0=180\u00b0
\u21d2\u03b1=180\u2218\u221230\u22182=75\u2218
PQ||SR
\u03b2=\u2220PRS=75\u00b0
]<\/p>\n\n\n\n

\n\n\n\n

TYPE 3<\/strong><\/p>\n\n\n\n

\n\n\n\n

QUESTION 12<\/h4>\n\n\n\n

In a parallelogram ABCD , bisectors of consecutive \u2220A and \u2220B intersect at a point P. Prove that \u2220APB=90\u00b0<\/strong>
\"\"
Sol :<\/p>\n\n\n\n

\n\n\n\n

QUESTION 13<\/h4>\n\n\n\n

If diagonals of a parallelogram bisect its angles , then prove that the diagonals will be perpendicular to each other.<\/strong>
Sol :<\/p>\n\n\n\n

\n\n\n\n

QUESTION 14<\/h4>\n\n\n\n

In  a quadrilateral ABCD , \u2220A=\u2220C and \u2220B=\u2220D , prove that ABCD is a parallelogram.
<fig to be added>
[Hint: In quadrilateral ABCD
\u21d2\u2220A+\u2220B+\u2220C+\u2220D=360\u00b0
\u21d2\u2220A+\u2220B+\u2220A+\u2220B=360\u00b0
\u21d22(\u2220A+\u2220B)=360\u00b0
\u21d2\u2220A+\u2220B=180\u00b0
\u21d2AD||BC
Now , on joining BD , we have
\u0394ABD\u2245\u0394CDB [AAS congruency rule]
ABCD is a parallelogram]
Sol :<\/p>\n\n\n\n

\n\n\n\n

QUESTION 15<\/h4>\n\n\n\n

Prove that the bisectors of angles of a parallelogram form a rectangle.<\/strong>
<fig to  be added>
[Hint: Bisectors of \u2220A and \u2220B meet at point S]
\u2220BAS+\u2220ABS=1\/2(\u2220A+\u2220B)
=1\/2 \u00d7180\u00b0 [AD||BC and AB is a transversal]
So , \u2220BAS+\u2220ABS=90\u00b0
In \u0394ABS , \u2220ASB=90\u00b0 ..(i)
\u2220PSR=90\u00b0 [vertically opposite angles]
Similarly , \u2220SRQ=90\u00b0 , \u2220RQP=90\u00b0 and \u2220QPS=90\u00b0
Hence ,PQRS is a rectangle ]
Sol :<\/p>\n\n\n\n

\n\n\n\n

QUESTION 16<\/h4>\n\n\n\n

In the given figure , ABC is a triangle and through vertices A, B and C  , three lines are drawn which are respectively parallel to opposite sides. Prove that the perimeter of the triangle DEF , so formed by these three lines is two times the perimeter of the triangle ABC.<\/strong>
<fig to be added>
[Hint: FA=BC; FB=AC; AE=BC
EC=AB; DC=AB; BD=AC
\u2234FA+FB+AE+EC+DC+BD=BC+AC+BC+AB+AB+AC
\u21d2(FA+AE)+(FBB+BD)+(EC+DC)=2(AB+BC+CA)
\u21d2EF+FE+ED=2(AB+BC+AC)
]
Sol :<\/p>\n\n\n\n

\n\n\n\n

QUESTION 17<\/h4>\n\n\n\n

ABCD is a parallelogram in which bisectors of \u2220A and \u2220C meet the diagonals BD at P and Q respectively. Prove that PCQA is a parallelogram.<\/strong>
Sol :<\/p>\n\n\n\n

\n\n\n\n

QUESTION 18<\/h4>\n\n\n\n

ABCD is a parallelogram and EF||BD.\u00a0 R is mid point of EF. Prove that BE=DF<\/strong>
\"ABCD
Sol :<\/p>\n\n\n\n

\n
KC Sinha Solutions<\/a><\/div>\n\n\n\n
KC Sinha Class 9 Solutions<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

EXERCISE 10.1 Type 1 QUESTION 1 Fill in the blanks:(i) A parallelogram will be a rhombus, if and only if its ___are Perpendicular to each other.(ii) A quadrilateral will be a parallelogram, if and only if its diagonals ___ each other.(iii) Opposite angles of a parallelogram are __Sol : QUESTION 2 Which of the following […]<\/p>\n","protected":false},"author":302,"featured_media":623886,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"newspack_featured_image_position":"","newspack_post_subtitle":"","newspack_article_summary_title":"Overview:","newspack_article_summary":"","newspack_hide_updated_date":false,"newspack_show_updated_date":false,"footnotes":""},"categories":[921],"tags":[],"boards":[],"class_list":["post-623881","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-9","entry"],"yoast_head":"\nKC Sinha: Exercise 10.1 - Mathematics Solution Class 9 Chapter 10 Quadrilaterals - 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