the diagonals of a quadrilateral abcd intersect each other at the point o such that
Mohammed
Guys, does anyone know the answer?
get the diagonals of a quadrilateral abcd intersect each other at the point o such that from screen.
The diagonals of a quadrilateral ABCD intersect each other at the point O such that AOBO = CODO . Show that ABCD is a trapezium.
Click here👆to get an answer to your question ✍️ The diagonals of a quadrilateral ABCD intersect each other at the point O such that AOBO = CODO . Show that ABCD is a trapezium.
Question BO AO = DO CO
. Show that ABCD is a trapezium.
Medium Open in App
Updated on : 2022-09-05
Given:Solution Verified by Toppr
The diagonals of a quadrilateral ABCD intersect each other at the point O such that
BO AO = DO CO i.e., CO AO = DO BO
To Prove: ABCD is a trapezium
Construction:
Draw OE∥DC such that E lies on BC.
Proof: In △BDC,
By Basic Proportionality Theorem,
OD BO = EC BE ............(1) But, CO AO = DO BO
(Given) .........(2)
∴ From (1) and (2) CO AO = EC BE
Hence, By Converse of Basic Proportionality Theorem,
OE∥AB Now Since, AB∥OE∥DC ∴ AB∥DC
Hence, ABCD is a trapezium.
Video Explanation
Solve any question of Triangles with:-
Patterns of problems
>
Was this answer helpful?
372 19
The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/BO=CO/DO . Show that ABCD is a trapezium.
The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/BO=CO/DO . Show that ABCD is a trapezium.
Byju's Answer Standard X Mathematics
Basic Proportionality Theorem
The diagonals... Question
The diagonals of a quadrilateral
ABCD
intersect each other at the point
O such that AOBO=CODO . Show that ABCD is a trapezium. Open in App Solution
Step 1. Explaining the diagram.
Let ABCD
be quadrilateral where
AC and BD
intersects each other at
O such that, AOBO=CODO
Step 2. ShowingABCD
is trapeziumConstruction-From the pointO , draw a line EO touching AD at E in such a way that, EO∥DC∥AB In ΔDAB, EO || AB
By using Basic Proportionality Theorem
DEEA=DOOB........................(i)
Also, given, AOBO=CODO
⇒AOCO=BODO [applying alternendo]
⇒COAO=DOOB [ [applying invertendo]
⇒DOOB =COAO..........................(ii)
From equation (i) and (ii), We have DEEA=COAO
Therefore, By applying converse of Basic Proportionality Theorem,
EO || DC Also
EO || AB ⇒ AB || DC.
Hence, quadrilateralABCD
is a trapezium withAB || CD.
Suggest Corrections 16
SIMILAR QUESTIONS
Q.ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that
Q. The diagonals of a quadrilateralA B C D
intersects each other at the point
O such that A O B O = C O D O . Show that A B C D is a trapezium.
Q. Question 10The diagonals of a quadrilateral ABCD intersect each other at the point O such that
A O B O = C O D O
. Show that ABCD is a trapezium.
Q. The diagonals of a quadrilateralA B C D
intersect each other at the point
O , such that A O B O = C O D O . Then A B C D is a trapezium.
Q.A B C D
is a trapezium in which
A B | | D C
and its diagonals intersect each other at point
′ O ′ . Show that A O B O = C O D O . View More RELATED VIDEOS
Basic Proportionality Theorem
MATHEMATICS Watch in App EXPLORE MORE
Basic Proportionality Theorem
Standard X Mathematics
Ex 6.2, 10
Ex 6.2, 10 The diagonals of a quadrilateral ABCD intersect each other at the point O such that 𝐴𝑂/𝐵𝑂 = 𝐶𝑂/𝐷𝑂 . Show that ABCD is a trapezium Given: ABCD is a quadrilateral where diagonals AC & BD intersect at O & 𝐴𝑂/𝐵𝑂=𝐶𝑂/𝐷𝑂 To prove: ABCD is a trapezium Construction: Let us draw a lin
Ex 6.2, 10 - Chapter 6 Class 10 Triangles (Term 1)
Last updated at March 16, 2023 by Teachoo
Ads by
Ad
This video is only available for Teachoo black users
Subscribe Now
Get live Maths 1-on-1 Classs - Class 6 to 12
Book 30 minute class for ₹ 499 ₹ 299
Transcript
Ex 6.2, 10 The diagonals of a quadrilateral ABCD intersect each other at the point O such that 𝐴𝑂/𝐵𝑂 = 𝐶𝑂/𝐷𝑂 . Show that ABCD is a trapezium Given: ABCD is a quadrilateral where diagonals AC & BD intersect at O & 𝐴𝑂/𝐵𝑂=𝐶𝑂/𝐷𝑂 To prove: ABCD is a trapezium Construction: Let us draw a line EF II AB passing through point O. Proof: Given 𝐴𝑂/𝐵𝑂=𝐶𝑂/𝐷𝑂 ⇒ 𝐴𝑂/𝐶𝑂=𝐵𝑂/𝐷𝑂 Now, in ∆ 𝐴𝐷𝐵 EO II AB 𝐴𝐸/𝐷𝐸=𝐵𝑂/𝐷𝑂 ⇒ 𝐴𝐸/𝐷𝐸=𝐴𝑂/𝐶𝑂 Thus in Δ ADC, Line EO divides the triangle in the same ratio ∴ EO II DC Now, EO II DC But, we know that EO II AB ⇒ EO II AB II DC ⇒ AB II DC Hence, one pair of opposite sides of quadrilateral ABCD are parallel Therefore ABCD is a trapezium . Hence proved
Next: Ex 6.3 →Ask a doubt Facebook Whatsapp
Made by
Davneet Singh
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.
Guys, does anyone know the answer?