Fill in the blanks using correct word given in the bracket:
All circles are __________. (congruent, similar)
All squares are __________. (similar, congruent)
All __________ triangles are similar. (isosceles, equilateral)
Fill in the blanks using correct word given in the bracket
Two polygons of the same number of sides are similar, if their corresponding sides are __________. (equal, proportional)
Two polygons of the same number of sides are similar, if their corresponding angles are __________ (equal, proportional)
Find the similar figures.
Find the non-similar figures.
State whether the following quadrilaterals are similar or not:
The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/BO = CO/DO. Check if ABCD is a trapezium.
E and F are points on the sides PQ and PR respectively of a ΔPQR. For PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm , state whether EF || QR.
In figure, DE || BC. Find AD.
E and F are points on the sides PQ and PR respectively of a ΔPQR. For PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm ,state whether EF || QR.
In figure DE || BC. Find EC.
E and F are points on the sides PQ and PR respectively of a ΔPQR. For PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm ,state whether EF || QR.
In the figure, if LM || CB and LN || CD, Check if AM/AB = AN/AD
In the figure, DE||AC and DF||AE. Check if BF/FE = BE/EC
In the figure, DE||OQ and DF||OR, Check if EF||QR.
In the figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Check if BC || QR.
ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Check if AO/BO = CO/DO.
In the given figure, \frac{QR}{QS}=\frac{QT}{PR} and ∠1 = ∠2. Check if ΔPQS ~ ΔTQR.
In the figure, ABC and AMP are two right triangles, right angled at B and M respectively, state whether ΔABC ~ ΔAMP.
In the figure, ABC and AMP are two right triangles, right angled at B and M respectively, state whether \frac{CA}{PA}=\frac{BC}{MP}
In the figure below, altitudes AD and CE of ∆ABC intersect each other at the point P. Check whether ΔAEP ~ ΔADB
E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. State whether if ΔABE ~ ΔCFB.
In the figure, ΔODC ~ ΔOBA, ∠ BOC = 125° and ∠ CDO = 70°. Find ∠ DOC, ∠ DCO and ∠ OAB.
In the figure below, altitudes AD and CE of ∆ABC intersect each other at the point P. Check whether ΔPDC ~ ΔBEC
In the following figure, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, state whether ΔABD ~ ΔECF.
CD and GH are respectively the bisectors of ∠ACB and ∠EGF such that D and H lie on sides AB and FE of ΔABC and ΔEFG respectively. If ΔABC ~ ΔFEG, check whether \frac{CD}{GH}=\frac{AC}{FG}
In the figure, if ΔABE ≅ ΔACD, state whether ΔADE ~ ΔABC.
In the figure below, altitudes AD and CE of ∆ABC intersect each other at the point P. Check whether ΔABD ~ ΔCBE
CD and GH are respectively the bisectors of ∠ACB and ∠EGF such that D and H lie on sides AB and FE of ΔABC and ΔEFG respectively. If ΔABC ~ ΔFEG, check whether ΔDCB ~ ΔHGE or not.
CD and GH are respectively the bisectors of ∠ACB and ∠EGF such that D and H lie on sides AB and FE of ΔABC and ΔEFG respectively. If ΔABC ~ ΔFEG, check whether ΔDCA ~ ΔHGF
Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. State whether ΔABC ~ ΔPQR.
D is a point on the side BC of a triangle ABC such that ∠ADC = ∠BAC. Check if that CA2 = CB.CD
A vertical pole of a length 6 m casts a shadow 4m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.
If AD and PM are medians of triangles ABC and PQR, respectively where ΔABC ~ ΔPQR state whether \frac{AB}{PQ}=\frac{AD}{PM}.
Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Using a similarity criterion for two triangles, check if the following statement is true or false:
\frac{AO}{OC}=\frac{OB}{OD}
S and T are point on sides PR and QR of ΔPQR such that ∠P = ∠RTS. Check if ΔRPQ ~ ΔRTS.
Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ΔPQR (see Fig). State whether ΔABC ~ ΔPQR.
State if the triangles are similar:
Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2CD, find the ratio of the areas of triangles AOB and COD.
Let ΔABC ~ ΔDEF and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC.
In the figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, check if the \frac{\text{area }ΔABC}{\text{area }ΔDBC} = \frac{AO}{DO} .
If the areas of two similar triangles are equal, by which criterion are they congruent.
D, E and F are respectively the mid-points of sides AB, BC and CA of ΔABC. Find the ratio of the area of ΔDEF and ΔABC.
ABC and BDE are two equilateral triangles such that D is the mid-point of BC and E is the mid-point of AB. Ratio of the area of triangles ABC and EBD is
Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio
Two poles of heights 9 m and 14 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.
Sides of triangles are 3 cm, 8 cm, 6 cm. Determine if right triangle? In case of a right triangle, write the length of its hypotenuse.
Sides of triangles are 50 cm, 80 cm, 100 cm . Determine if right triangle? In case of a right triangle, write the length of its hypotenuse.
An aeroplane leaves an airport and flies due north at a speed of 1,000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1,200 km per hour. How far apart will be the two planes after 1 (1/2) hours ?
In ΔABC, AB = 6√3 cm, AC = 12 cm and BC = 6 cm. The angle B is
Sides of a triangle are 13 cm, 12 cm, 5 cm. If the given triangle is a right angled triangle, find the length of its hypotenuse.
PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR. State whether PM2 = QM × MR.
In Figure, ABD is a triangle right angled at A and AC ⊥ BD. State whether AB2 = BC × BD
ABC is an equilateral triangle of side 2a. Find its altitude.
If ABC is an isosceles triangle with AC = BC. If AB2 = 2AC2, state which statement is true.
A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from base of the wall.
A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?
Sides of a triangle are 7 cm, 24 cm, 25 cm. If the given triangle is a right angled triangle, find the length of its hypotenuse.
In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a …… angle.
A 6.5 m long ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall. Find the height of the wall where the top of the ladder touches it.
If ABC is an isosceles triangle right angled at C, then AB2 =
In the given figure, D is a point on hypotenuse AC of ∆ABC, such that BD ⊥AC, DM ⊥ BC and DN ⊥ AB. Check if DN2 = DM . AN.
In Figure, PS is the bisector of ∠ QPR of ∆ PQR. State whether QS/PQ = SR/PR.
In the given figure, D is a point on hypotenuse AC of ∆ABC, such that BD ⊥AC, DM ⊥ BC and DN ⊥ AB. Check if DM2= DN . MC
In the figure below, two chords AB and CD intersect each other at the point P. State what is AP . PB =
In the figure, two chords AB and CD of a circle intersect each other at the point P (when produced) outside the circle. By which criterion, the two triangles ∆ PAC and ∆ PDB are similar?
In the figure, two chords AB and CD of a circle intersect each other at the point P (when produced) outside the circle.
Complete the given statement AP. PB =
Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, how much string does she have out (see Figure)?
Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, the length of the string is 3m. If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds? (see Figure)?
In Figure, AD is a median of a triangle ABC and AM ⊥ BC. State whether AC2 = AD2 + BC.DM + 2 (BC/2) 2 is true or false.
In the figure below, two chords AB and CD intersect each other at the point P. State ∆APC ~ ∆____.
In Figure, AD is a median of a triangle ABC and AM ⊥ BC. State whether AB2 = AD2 – BC.DM + 2 (BC/2) 2 is true or false.
In Figure, AD is a median of a triangle ABC and AM ⊥ BC. State whether AC2 + AB2 = 2 AD2 + ½ BC2 is true or false.
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