Write the Correct answer
0 of 38 Questions completed
Questions:
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading…
You must sign in or sign up to start the quiz.
You must first complete the following:
0 of 38 Questions answered correctly
Your time:
Time has elapsed
You have reached 0 of 0 point(s), (0)
Earned Point(s): 0 of 0, (0)
0 Essay(s) Pending (Possible Point(s): 0)
Average score |
|
Your score |
|
In the figure, \(\angle M=\angle N=46^o \). Express \(x \) in terms of a, b and c, where a, b and c are lengths of \(LM, MN \) and \(NK \) respectively.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In and
(Corresponding angle)
(Common)
(AA similarly)
In the figure, LM || CB and LN || CD, prove that \(\dfrac{AM}{AB}=\dfrac{AN}{AD} \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
(1) In
…(1)
In
….(2)
From (1) and (2)
In the given figure, ABC and AMP are two right triangles, right angled at B and M respectively. Prove that :
(i) \(\triangle ABC\sim\triangle AMP \)
(ii) \(\dfrac{CA}{PA}=\dfrac{BC}{MP} \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In and
(each
)
(common)
(AA similarly)
(Corresponding sides of similar triangles are proportional)
In the figure, DE || OQ and DF || OR. Show that EF || QR.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In
…(1) (using BPT)
In
…(2) (using BPT)
comparing (1) and (2)
(by converse of BPP)
By using the converse of the basic proportionality theorem, show that the line joining mid-points of non-parallel sides of a trapezium is parallel to the parallel sides.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In and
(
is mid point of
)
(alt opp
)
(ASA)
and In
as
and
i.e.
Hence
If three or more parallel lines are intersected by two transversals, the intercepts made by them on the transversal are proportional. Prove.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In
(using BPT) ….(1)
In
…(2) (using BPT)
From (1) and (2)
(Proved)
\(ABC \) is a triangle in which \(\angle A=90^o,\ AN\bot BC,\ AB=12\ cm \) and \(AC=5\ cm \). Find the ratio of the area of \(\triangle ANC \) and \(\triangle ABC \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In and
(common)
(each
)
(AA similarly)
ABCD is a square. F is the mid-point of AB.BE is the one-third of BC. If the area of the \(\triangle \)BFE is \(108\ cm^2\), find the length of AC.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Area of
In the given figure, \(\angle B<90^o \) and segment \(AD\bot BC \), show that \(b^2=h^2+a^2+x^2-2ax \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
(
is equilateral)
(common)
(AAS)
In
Using BPT, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
(using BPT)
or is the mid point of
If \(\triangle ABC\sim\triangle DEF \) and, \(AL \) and \(DM \) are their corresponding medians, then show that \(\dfrac{AL}{DM}=\dfrac{AB}{DE}=\dfrac{BC}{EF}=\dfrac{AC}{DF} \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
(given)
(AA)
….(1)
In and
(given)
(AA)
….(2)
From (1) and (2)
If \(\triangle ABC\sim\ \triangle DEF \), then show that \(\dfrac{perimeter\ of\ \triangle ABC}{perimeter\ of\ \triangle DEF}=\dfrac{AB}{DE}=\dfrac{BC}{EF}=\dfrac{AC}{DF} \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
….(1)
…(2)
….(3)
Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 3CD, find the ratio of the areas of triangles AOB and COD.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In and
(AA)
In \(\triangle \)ABC, in figure, PQ meets AB in P and AC in Q. If If AP = 1 cm, PB = 3 cm, AQ = 1.5 cm, QC = 4.5 cm, prove that area of \(\triangle \)APQ is one sixteenth of the area of \(\triangle \)ABC.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In and
(common)
(SAS)
In the figure, PA, QB and RC are perpendiculars to AC. Prove that \(\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{z} \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Let
In and
(common)
(each
)
(AA)
…(1)
Similarly (AA)
…(2)
Adding eqn (1) and (2)
In an equilateral triangle \(ABC, D\) is a point on side \(BC \) such that \(3BD = BC\). Prove that \(9AD^2=7AB^2\).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In and
(common)
(RHS)
(cpct)
In
In \(\triangle \)PQR,PD \(\bot \) QR such that D lies on QR. If PQ = a, PR = b, QD = C and DR = d and a, b, c, d are positive units, prove that (a+b) (a-b) = (c+d) (c-d).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In
….(1)
In
…(2)
From (1) and (2)
In figure, \(BL \) and \(CM \) are medians of \(\triangle ABC \). right angled at \(A \). Prove that \(4(BL^2+CM^2) = 5BC^2\)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In
In
In the figure, ABC is an isosceles triangle right angled at B. Two equilateral triangles are constructed with side BC and AC. Prove that : \(\mathrm{ar\ \triangle BCD=\dfrac{1}{2}ar\ \triangle ACE} \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
…(1)
In figure, ABC is right triangle right angled at C. Let BC = a, CA = b, AB = c and let p be the length of perpendicular from C on AB. Prove that
(i) \(cp=ab \)
(ii) \(\dfrac{1}{p^2}=\dfrac{1}{a^2}+\dfrac{1}{b^2} \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Area of
Area of
So,
In the figure, PQR is a triangle in which \(QM\bot PR \) and \(PR^2-PQ^2=QR^2 \), prove that \(QM^2=PM\times MR \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
….(1)
In
…(2)
From (1) and (2)
In figure, DE || BC and AD : DB = 5 : 4. Find \(\dfrac{ar(\triangle DFE)}{ar(\triangle CFB)} \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
…(1)
In and
(alt.
)
(VOA)
In the figure, \(PQR \) is a right angled triangle in which \(Q=90^o \). If \(QS=SR \), show that \(PR^2-4PS^2=3PQ^2 \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In the figure, l || m and line segments AB, CD and EF are concurrent at P. Prove that : \(\dfrac{AE}{BF}=\dfrac{AC}{BD}=\dfrac{CE}{FD} \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In and
(VOA)
(alt
)
(AAA)
…(1)
In and
(VOA)
(alt.
)
(AA)
….(2)
Similarly ….(3)
From (1), (2), (3)
In the figure, \(\angle QPR=90^o,\angle PMR=90^o,\ QR=26\ cm,\ PM=8\ cm,\ MR=6\ cm \). Find area \((\triangle PQR) \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In
Area of
In \(\triangle \)ABC,D and E are two points lying on side AB such that AD = BE. If DP||BC and EQ || AC, then prove that PQ||AB.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In ,
and
and
and
So by the converse of BPT
Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
and
In
In the figure, \(DEFG \) is a square and \(\angle BAC=90^o \). Show that \(DE^2=BD\times EC \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In and
(Corresponding angles)
(AA) …(1)
In and
(corresponding angles)
(AA)….(2)
From (1) and (2)
(DEFG is a square)
In the figure, \(\triangle PQR \) is right angled at \(Q \) and the points \(S \) and \(T \) trisect the side \(QR \). Prove that \(8PT^2=3PR^2 + 5PS^2 \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Let
and
In
In
In
In the given figure, O is a point in the interior of a triangle ABC, OD \(\bot \) BC,OE \(\bot \) AC and OF \(\bot \) AB. Show that
(i) \(OA^2+OB^2+OC^2-OD^2-OE^2-OF^2= AF^2+ BD^2+CE^2 \)
(ii) \(AF^2 + BD^2 + CE^2 = AE^2 + CD^2 + BF^2 \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
…(1)
…(2)
…(3)
Adding (1), (2), (3) we get
(Proved)
(ii) From (1) we have
(Proved)
In a right triangle ABC, right angled at C. P and Q are points on the sides CA and CB respectively which divide these sides in the ratio 1 : 2. Prove that :
(i) \( 9AQ^2 = 9AC^2 + 4BC^2 \)
(ii) \(9BP^2 = 9BC^2 + 4AC^2 \)
(iii) \(9(AQ^2 + BP^2) = 13AB^2 \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
(i) (Proved) ….(1)
(ii) In ….(2)
(ii) Adding (1) and (2)
In the given figure, in \(\triangle \)PQR XY || QR. PX = 1 cm, XQ = 3 cm, YR = 4.5 cm and QR = 9 cm. Find PY and XY. Further if the area of \(\triangle \)PXY is ‘A’ \(cm^2 \), find in terms of A the area of \(\triangle \)PQR and the area of trapezium XYRQ.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In and
(corresponding angles)
(AA)
If A be the area of a right triangle and a one of the sides containing the right angle, prove that the length of the altitude on the hypotenuse is \(\dfrac{2Aa}{\sqrt{a^4+4A^2}} \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Base of the right angled unit
Area
Altitude
Prove that if a line is drawn parallel to one side of a triangle to intersect the other sides in distinct points, the other two sides are divided in the same ratio.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Area of
area of ….(1)
Also area of …(2)
Similarly …(3)
….(4)
Dividing (1) by (3) we get
…(5)
Again dividing (2) by (4) we get
….(6)
…(7)
From (5), (6), (7) we get (Proved)
State and prove converse of Pythagoras theorem.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Area of
area of ….(1)
Also area of …(2)
Similarly …(3)
….(4)
Dividing (1) by (3) we get …(5)
Again dividing (2) by (4) we get ….(6)
…(7)
From (5), (6), (7) we get (Proved)
By BPT
Adding on both the sides
is isosceles
Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
Using the above result do the following :
In the figure, DE || BC and BD = CE.
Prove that \(\triangle \)ABC is an isosceles triangle.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In and
(alt
)
(AAS)
(cpct)
(
is a parallelogram)
In and
(VOA)
(alt
)
(AA)
Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in L and AD produced in E. Prove that EL = 2BL.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
In a triangle if the square of one side is equal to the sum of the square of the other two sides then the angle opposite to the first side is a right angle
To prove
Proof …(1) (
Since
and
)
But (given) …(2)
From (1) and (2)
In and