QUADRILATERAL
1) In the given figure,
ABCD is a parallelogram in which angle A=74°. Calculate angle B, C, D.
2) in the given figure
ABCD is a parallelogram in which angle DAB=70°, angle DBC=50°. Compute ang CDB, ADB.
ABCD is a parallelogram in which angle DAB=70°, angle DBC=50°. Compute ang CDB, ADB.
3) In the given figure,
ABCD is a parallelogram in which Angle DAP= 20°, angle BAP= 40° and angle ABP= 80°. Find angle APD, BPC.
4) ABCD is a parallelogram. If AB= 2AD and P is the midpoint of AB, then find angle CPD.
5) if an angle of a parallelogram is two-thirds its adjacent angle, find the angles of the parallelogram.
6) Find each of a parallelogram if two consecutive angles are in the ratio 1:5.
7) Find the measures of an angle of a parallelogram if one angle is 30° less than twice the smallest angle.
8) In the given figure,
ABCD is a parallelogram with perimeter 40cm. Find the value of x and y.
9) In the following figures , find the value of x, y and z.
10) In the given figure,
ABCD is a parallelogram. P and Q are the made points of BC and AD respectively. Prove that APCQ is a parallelogram.
11) ABCD is a parallelogram and points P and Q are the points on the sides AD and BC respectively, such that AP= 1/4 AD and CQ= 1/4 BC. Prove that BPDQ is a parallelogram.
12) ABCD is a parallelogram.
BM bisects angle ABC and DN bisects angle ADC. Prove that BNDM is a parallelogram and BM= DN
Continue.....
1) 106, 74,106 2) 60,50 3) 40,80 4) 90 5) 72,108,72,108 6) 30,150,30,150 7) 70,110,70,110 8) 4,5 9)
MID-POINT THEOREM
Multiple Choice Questions (Quadrilateral & Mid-point)
1) Three angles of a quadrilateral are 60°, 86° and 110°. The fourth angle is
a) 104° b) 124° c) 94° d) 84°
2) The value of x in the given figure
is
a) 10 b) 20 c) 30 d) 40
3) In a quadrilateral , three angles are in the 3: 3 :1 and the fourth angle is 80°, then the other angle are
a) 100°, 100°, 80° b) 120°, 120°, 40° c) 100°,110°,70° d) 110°,110°,60
4) In a quadrilateral ABCD, AB|| DC and AD= BC= 5.5cm, and one of the angles is 80°, then the other angles are
a) 90°, 90°, 100° b) 120°, 80°, 80° c) 80°,100°,100° d) 110°,85°,85°
5) The sides of a quadrilateral are extended in order to form exterior angles . The sum of these exterior angles is
a) 360° b) 270° c) 90° d) 180°
6) Which of the following is not true for a parallelogram ?
a) opposite sides are equal.
b) opposite angles are equal
c) opposite angles are always bisected by the diagonals.
d) diagonals bisect each other.
7) in a quadrilateral ABCD, if AB= BC and CD= DA, then quadrilateral ABCD is a
a) trapezium b) rhombus c) kite d) parallelogram
8) Given a quadrilateral ABCD such that angle C=90° and diagonals AC and BD bisect each other at right angles, then the quadrilateral is a
a) trapezium b) kite c) rectangle d) square
9) P and Q are the mid-points of the sides AB and AC of ∆ ABC and O is any point on side BC . O is joined to A. If S and R are the midpoints of OB and OC respectively, then PQRS is
a) a square b) a rectangle c) a Rhombus d) a parallelogram
10) if bisectors of angle P and Q of a quadrilateral PQRS intersect each other at A, of angle Q and R at B, of angle R and S at C and of angle S and P at D, then ABCD is a
a) rectangle b) rhombus c) parallelogram
d) quadrilaterals whose opposite angles are supplementary.
11) ABCD is a Rhombus in angle BCD= 100°, then (x + y) equals
a) 40 b) 69 c) 80 d) 70
12) ABCD is a parallelogram. If angle A= (3x -20)° and angle C= (x +40)°, then the value of x is
a) 30 b) 40 c) 50 c) 60
13) D and E are the midpoints of the side AB and AC respectively of ABC DE is produced to F. To prove that DA is equal and parallel to FC, we need an additional information, which is
a) angle DAE= angle EFC b) AE= EF c) DE= EF d) angle ADE= angle ECF
14) ABCD is a parallelogram. If its diagonals are equal, then the measure of angle ABC is
a) 60 b) 90 c) 75 d) 120
15) Diagonals AC and BD of a parallelogram ABCD interesect each other at O. If OA= 5cm and OD= 4cm, then the length of AC and BD respectively are
a) 5cm, 4cm b) 10cm, 8cm c) 2.5 cm, 2cm d) 15cm, 12cm
16) If the angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 60°, then the angles of the parallelogram are
a)105°, 75°, 105°, 75° b) 115°, 65°, 115°, 65° c) 120°,60°, 120°,60° d) 110°,70°, 110°,70°
17) In a parallelogram, if angle A=60°, then angle D is equals to
a) 110° b) 140° c) 120° d) 130°
18) One angle of a quadrilateral is 114° and the remaining three angles are equal. Then , the measure of each of the three equal angles is
a) 82° b) 84° c) 86° d) 92°
19) Given a trapezium PQRS such that PQ= 12cm, RS= 5cm, PQ|| SR, PS= QR= 8cm. If angle R= 130, then angle P is
a) 130 b) 50 c) 150 d) 120
20) In a parallelogram ABCD, AB= 3cm and the diagonals AC and BD are 5.8 cm and 4.2 respectively. If the diagnols AC and BD interesect at O, then the perimeter of ∆ AOB is
a) 10cm b) 8.8cm d) 7.28cm
21) If an angle of a parallelogram is four-fifths of its adjacent angle, then the angles of the parallelograms are
a) 70°, 110°, 70° , 110°
b) 80°, 100°, 80°, 110
c) 72°,118°,72°, 108°
d) 60°,120°,60°, 120°
22) Four angles of a quadrilateral are (2x +20)°, (3x -30)°, (x +10)° and (2x)°. Value of x is
a) 40 b) 45 c) 50 d) 55
23) ABCD is a rectangle where BC= (4x -5)cm and AD= (2x +3)cm. Then, BC is
a) 11cm b) 12cm c) 10cm d) 15cm
24) In Rhombus PQRS , PQ= 3x, QR=2(x +3)cm. Each side of the Rhombus is
a) 17 b) 19cm c) 18cm d) 28cm
25) ABCD is a rhombus in which altitude from D to side AB bisect AB. Then the angles of the rhombus
a) 100°, 80°, 100°, 80°
b) 110°, 70°, 110°, 70°
c) 120°,60°,120°,60°
d) 130°,50°,130°, 50°
26) P is the midpoint of side BC of a parallelogram ABCD such that angle BAP= Angle DAP. If AD= 10cm, then length of CD is
a) 10cm b) 5cm c) 6cm d) 8cm
27) ABCD is a parallelogram. P and Q are respectively the mid-points of AB and CD . PQ and diagonal AC intersect at M. If AM= 3cm, then the length of the diagonals AC is
a) 3 cm b) 4.5cm c) 6 cm d) 7.5cm
28) The diagonals AC and BD of a parallelogram ABCD intersect each other at point O. If angle BOA= 68° and angle CAD= 25°, then angle DBC is equals to
a) 40 b) 43 c) 68 d) 25
29, in a parallelogram PQRS, PQ= 9cm and PS= 5 cm. The bisector of angle P meets SR in A. PA and QR produced meet at B. Then, the length of RB is
a) 5cm b) 4cm c) 9cm d) 6cm
30) M is the mid point of side CD of a parallelogram ABCD. A line through C parallel to MA intersect AB at P and DA produced at R. If DA = 3.5cm, then the length of DR is
a) 3.5cm b) 5cm c) 7cm d) 10.5cm
31) ABCD is a trapezium in which AB|| DC. M and N are the midpoints of AD and BC respectively. If AB=12 cm, MN= 14cm, then the length of CD is
a) 16cm b) 14 cm c) 12cm d) 10cm
32) PQRS is a parallelogram. A and B are respectively the midpoints of the sides PQ and SR. AS and BQ meet the diagonal PR of length 12cm at C and D respectively. Then , the length of CD is
a) 6cm b) 3cm c) 4cm d) 5cm
33) The side AB of the parallelogram ABCD is produced to X and the bisectors of angle CNX meets DA produced and DC produced at E and F respectively. If DE= 10cm, then the length of DF is
a) 5cm b) 10cm c) 7.5cm d) 15cm
34) If the Diagonals of a rhombus are 18cm and 24cm respectively, then its side is equals to
a) 16cm b) 15cm c) 20 cm d) 17cm
35) In ∆ ABC , angrA, B & C are 30°, 40°, 110°. Then, the angles of the triangle formed by joining the midpoint of the sides of the triangle are
a) a) 70°, 70°, 40° b) 60°, 40°, 80° c) 30°,40°,110° d) 60°,70°,50°
1a 2b 3b 4c 5a 6c 7c 8d 9d 10d 11c 12a 13c 14b 15b 16c 17c 18a 19b 20d 21b 22b 23a 24c 25c 26b 27c 28b 29b 30c 31a 32c 33b 34b 35cq
SHORT ANSWER QUESTIONS
1) In the adjoining figure,
AB|| QP|| CD, Q is the midpoint of AC. If AB = 4cm, CD= 6cm, find the measure of PQ.
2) In the given figure,
ABC is an equilateral triangle. O is a point inside ∆ ABC. P, Q and R are the midpoints of AO, BO and CO respectively. Find the measures of x, y and z.
3) In the given figure,
D and E are midpoints of the sides AB and AC respectively of ∆ ABC. Q is any point on BC. AQ interesects DE at P. If AP= 3cm, find the measure of AQ.
4) In the given figure,
the straight lines l, m and n, are parallel to each other and G is the midpoint of CD. Calculate :
a) BG, if AD= 7cm
b) CF, if GE= 2.5cm
c) AB, if AC= 9cm
d) ED, if FE= 4cm.
5) ABCD is a quadrilateral,
P,Q,R and S are the midpoints of AB, BC CD and DA respectively. If AC= 6cm, BD=8.6cm, calculate PQ, QR, SR & PR.
6) Diagonals AC and BD of a quadrilateral ABCD intersect each other at O such that OA: OC = 2:3. Is ABCD a parallelogram ? justify your answer.
7) ABCD and AEFG are two parallelograms.
If angle C= 58°, determine angle F.
If angle C= 58°, determine angle F.
8) Angles of a quadrilaterals are in the ratio 3:4:4:7. Find all the angles of the quadrilateral.
9) In the given figure,
ABCD is a parallelogram. AX and CY are respectively the bisectors of opposite angles A and C. If angle DCB = 80°, find the measures of angle DAX.
10) ABC is a triangle and through A, B and C lines are drawn parallel to BC, CA, AB respectively intersecting at P, Q, R. if the perimeter of triangle PQR is 48cm, then find the perimeter of ∆ ABC.
1) 5cm 2) 20,25,20 3) 6cm 4) 3.5,5,4.5,4 5) 3.5, 5, 4.5,4 6) no 7) 58° 8) 60,80,80,140 9) 40 10) 24cm
VALUE - BASED QUESTIONS
1) The sports teacher and students class IX were in the process of preparing a drill for the sports day. An equilateral ∆ ABC was marked on the ground for some students to stand along its sides AB, BC, CA. The teacher wanted another smaller equilateral triangle PQR drawn within ∆ ABC along whose sides the remaining students could stand. The students suggested taking points P,Q, R as midpoints of AB, AC & BC and then joining PQ, QR, & PR.
i) Where the students right ? justify your answer.
ii) Write two values exhibited by the students.
2) ABCD is a rhombus
in which angle ABC= 110°. Ram's house is located at point A and Anil's house is situated at point B. There is an old age home at point O.
i) If Ram and Anil go along OA and BO respectively to reach there every Sunday to help out the senior citizens living there, then which of them has to cover shorter distance to reach there ?
ii) What values of shown by Ram and Anil ?
1)i) Yes , the students were correct
PQ= 1/2 BC, QR= 1/2 AB and PR= 1/2 AC, by mid-point theorem
ii) Problem-solving and helpfulness.
2) i) Anil has to cover a shorter distance than Ram.
As angle AOB= 90, angle BAO= 35, angle ABO= 55, BO< AO)
ii) emphaty, concern for senior citizens, helpfulness , responsibility and carying for others.
UNIT TEST
Is a parallelogram 65 = 180 150 150 quadrilateral the diagonals are equal then it cannot be square parallelogram numbers rectangle diagonals of the parallelogram intersect 90 and 50 then 40 50 10 90 a transversals to parallel lines the tool interior angles at bisector so are the two integer angles at the 4 by sector 56 quadrilateral which is trapezium rumble to the triangle in the given figure is a rhombus 4 and 3 then the perimeter the numbers is 18 20 21 22 parallelogram of the angles ABCD is a parallelogram bisector 6 find the measure of prove that the straight lines on in the midpoint of opposite sides of parallelogram sub parallel to other pair of parallel sides in the given figure find the perimeter of in the adjoining figure are two Triangles of the same side the midpoint respectively find the measure of X and Y in the given figure 6810 15 to find the measure of in the given figure is the mid point of and find the measure in a given figure is the midpoint 610 find the measure in the sun figure is a parallelogram is a midpoint Food line is on parallel to meet produce the five find the measure of the given figure a rectangles where is the mid point 5 minutes any straight line that makes in points respectively find the length ABC is an isosceles triangle is in which are the midpoint sick respectively name the type of quadrilateral formed by find the length at the points of tric section of the diagonals of the parallelogram prove that parallel also prove that biceps so that if the dimension of quadrilaterals are equal and bisect each other at right angle then its square in the given figure is produced to these the midpoint produced in NEET are drawn parallelproof are the midpoints of the sides respectively on isosceles group that are isosceles in the given figure is a parallelogram is don't parallel to reduce that it cut prove that given parallel lines are drawn through respectively the sides forming prove that is a parallelogram are respectively the angle bisector of is drawn parallel Prove Prove that the line segment joining the midpoint of the diagonals of a trapezium is parallel to the parallel equal to the half of the depress
No comments:
Post a Comment