Question 1 :
State true or false : A quadrilateral is a parallelogram, if its opposite angles are unequal.
Question 2 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d20af59b460d7261f527.PNG' />
Using the above fig, identify the quadrilateral formed by the angular bisectors of all the angles of a parallelogram.
Question 3 :
ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Is MD ⊥AC ?
Question 4 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d158f59b460d7261f427.jpg' />
In the above figure, X and Y are respectively the mid-points of the opposite sides AD and BC of a parallelogram ABCD. Also, BX and DY intersect AC at P and Q, respectively.Which statement is true for the given parallelogram?
Question 5 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d21ef59b460d7261f544.PNG' />
In the above fig, ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F. F ____________ BC.
Question 6 :
State true or false : The quadrilateral formed by joining the mid-points of the sides of a quadrilateral, taken in order, is a parallelogram.
Question 7 :
The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if
Question 8 :
State true or false: If all the points are collinear (in the same line), we obtain a line segment.
Question 9 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d202f59b460d7261f51d.PNG' />
In the fig shown above, (v) is a ___________ ?
Question 10 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d219f59b460d7261f53d.PNG' />
In ∆ ABC and ∆ DEF in the above fig, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively. Is ∆ ABC ≅ ∆ DEF ?
Question 11 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d201f59b460d7261f51b.PNG' />
Which of the fig shown above is a rectangle ?
Question 12 :
ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the $\angle ABC$ of the rhombus.
Question 13 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d203f59b460d7261f51f.PNG' />
Which of the two fig shown above has a smaller area ?
Question 14 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d208f59b460d7261f524.PNG' />
In the above fig, ABC is an isosceles triangle in which AB = AC. AD bisects exterior angle PAC and CD || AB . Is ∠ DAC = ∠ BCA ?
Question 15 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d154f59b460d7261f422.jpg' />
In the above figure, it is given that BDEF and FDCE are parallelograms. Can you say that BD = CD?
Question 16 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1fff59b460d7261f518.PNG' />
Which of the fig shown above is/ are quadrilaterals ?
Question 17 :
If bisectors of $\angle A$ and $\angle B$ of a quadrilateral ABCD intersect each other at P, of $\angle B$ and $\angle C$ at Q, of $\angle C$ and $\angle D$ at R and of $\angle D$ and $\angle A$ at S, then PQRS is a
Question 19 :
ABCD is a rectangle in which diagonal AC bisects ∠ A as well as ∠ C. Does the diagonal BD bisects ∠ B as well as ∠ D ?
Question 20 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d203f59b460d7261f51e.PNG' />
In the fig shown above, (vi) is a ___________ ?
Question 21 :
D and E are the mid-points of the sides AB and AC respectively of $\triangle ABC$. DE is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is
Question 22 :
ABCD is a rectangle in which diagonal AC bisects ∠ A as well as ∠ C. ABCD is a _________.
Question 23 :
State true or false : In a parallelogram diagonals bisect each other.
Question 24 :
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
Question 25 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d211f59b460d7261f532.PNG' />
In parallelogram ABCD shown in the fig above, two points P and Q are taken on diagonal BD such that DP = BQ. Is ∆ AQB ≅∆ CPD ?
Question 26 :
If APB and CQD are two parallel lines, then the bisectors of the angles APQ, BPQ, CQP and PQD form
Question 27 :
The figure formed by joining the mid-points of the sides of a quadrilateral ABCD, taken in order, is a square only if,
Question 28 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d213f59b460d7261f535.PNG' />
In parallelogram ABCD shown in the fig above, two points P and Q are taken on diagonal BD such that DP = BQ. Is AQ = CP ?
Question 29 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d20ef59b460d7261f52e.PNG' />
In the above fig, diagonal AC of a parallelogram ABCD bisects ∠ A. It bisects ∠ C. TRUE or FALSE ?
Question 30 :
If the diagonals of a quadrilateral bisect each other at right angles, then it is a ________.
Question 31 :
A diagonal of a parallelogram divides it into two ____________ triangles.
Question 32 :
A diagonal of a rectangle is inclined to one side of the rectangle at $25^{\circ}$. The acute angle between the diagonals is
Question 33 :
State true or false : A diagonal of a parallelogram divides it into two congruent triangles.
Question 34 :
E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. What would be shape of BFDE?
Question 35 :
ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. The quadrilateral PQRS is a ________________.
Question 36 :
P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD in which AC = BD. Quadrilateral formed by joining P,Q,R and S would be
Question 37 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d209f59b460d7261f526.PNG' />
In the above fig, two parallel lines l and m that are intersected by a transversal p are shown. The quadrilateral formed by the bisectors of interior angles is a ____________.
Question 38 :
If ABCD is a quadrilateral in which $AB\parallel DC$ and AD = BC, then which of the following statement is true?
Question 39 :
ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the $\angle ADC$ of the rhombus.
Question 40 :
If the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a __________.
Question 41 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d204f59b460d7261f520.PNG' />
Using the above fig, we can say that if each pair of opposite sides of a quadrilateral is equal, then it is a _______________.
Question 42 :
P and Q are the mid-points of the opposite sides AB and CD of a parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R. What type of quadrilateral would be PRQS?
Question 43 :
In $\triangle ABC$, AB = 5 cm, BC = 8 cm and CA = 7 cm. If D and E are respectively the mid-points of AB and BC, determine the length of DE.
Question 44 :
State true or false: If no three points out of four are collinear, we obtain a closed figure with four sides.
Question 45 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d216f59b460d7261f53a.PNG' />
In ∆ ABC and ∆ DEF in the above fig, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively. Quadrilateral ACFD is a ______________
Question 46 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1fef59b460d7261f517.PNG' />
In quadrilateral ABCD shown in the above fig, which of the following are its diagonals ?
Question 47 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d212f59b460d7261f534.PNG' />
In parallelogram ABCD shown in the fig above, two points P and Q are taken on diagonal BD such that DP = BQ. APCQ is a ______________.
Question 48 :
One angle of a quadrilateral is of $108^{\circ}$ and the remaining three angles are equal. Find each of the three equal angles.
Question 49 :
According to the Mid Point theorem, the line segment joining the mid-points of two sides of a triangle is ___________ to the third side and _______ of it.
Question 50 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d155f59b460d7261f423.jpg' />
In the above figure, through A, B and C, lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a ∆ ABC. What would the value of BC?
