Question 1 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c64273b230584979acc.PNG' />
In the above fig, altitudes AD and CE of ∆ ABC intersect each other at the point P. Is ∆AEP ~ ∆ADB ?
Question 2 :
E and F are points on the sides PQ and PR respectively of a ∆ PQR. State whether EF || QR if PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm
Question 4 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c44273b230584979aa6.PNG' />
ABCD is a trapezium as shown in the above fig with AB || DC. E and F are points on non-parallel sides AD and BC respectively such that EF is parallel to AB. Is $\frac{AE}{BF}$= $\frac{FC}{ED}$ ?
Question 6 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c45273b230584979aa8.PNG' />
Are the two triangles given in the above fig similar ?
Question 7 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b98273b2305849799d6.png' />
In the above given figure,$\angle$BAC = 90° and AD is perpendicular to BC. Then,
Question 9 :
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?
Question 10 :
In an equilateral triangle ABC, D is a point on side BC such that BD = $\frac{1}{3}BC$. Is $9 AD^2$ = $7 AB^2$ ?
Question 11 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b9d273b2305849799dd.png' />
If DE is parallel to BC, find the ratio of the area ADE and area DECB.
Question 12 :
If AD and PM are medians of triangles ABC and PQR, respectively where ∆ ABC ~ ∆ PQR, Is $\frac{AB}{PQ}$ = $\frac{AD}{PM}$ ?
Question 13 :
Let ∆ ABC ~ ∆ DEF and their areas be, respectively, 64 $cm^2$ and 121 $cm^2$ . If EF = 15.4 cm, find BC.
Question 14 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c5d273b230584979ac4.PNG' />
Are the triangles shown in the above fig similar ?
Question 15 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c62273b230584979aca.PNG' />
In the above fig, altitudes AD and CE of ∆ ABC intersect each other at the point P. Is ∆ABD ~ ∆ CEB ?
Question 16 :
CD and GH are respectively the bisectors of ∠ACB and ∠ EGF such that D and H lie on sides AB and FE of ∆ ABC and ∆ EFG respectively. If ∆ABC ~ ∆ FEG, is ∆ DCA ~ ∆ HGF ?
Question 17 :
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. Is ∆ABC ~ ∆ PQR ?
Question 18 :
State true or false:
In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Question 19 :
A ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall and its top reaches a window 6 m above the ground. Find the length of the ladder.
Question 20 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19ba3273b2305849799e4.png' />
If in the figure, PA, QB, RC and SD are all perpendiculars to a line l, AB = 6 cm, BC = 9 cm, CD = 12 cm and SP = 36 cm. Find PQ.
Question 21 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b99273b2305849799d7.png' />
In the given figure, two line segments AC and BD intersect each other at the point P such that PA = 6 cm, PB = 3 cm, PC = 2.5 cm, PD = 5 cm, $\angle$ APB = 50° and $\angle$ CDP = 30°. Then, $\angle$ PBA is equal to
Question 23 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19ba1273b2305849799e2.png' />
In the above figure, ABC is a triangle right angled at B and BD is perpendicular to AC. If AD = 4 cm, and CD = 5 cm, find BD.
Question 24 :
State True or False: In $\Delta$ ABC, AB = 24 cm, BC = 10 cm and AC = 26 cm. Then this is a right angled traingle.
Question 25 :
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. TRUE or FALSE?
Question 26 :
State true or false:
The area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.
Question 27 :
For going to a city B from city A, there is a route via city C such that AC is perpendicular to CB, AC = 2 x km and CB = 2 (x + 7) km. It is proposed to construct a 26 km highway which directly connects the two cities A and B. Find how much distance will be saved in reaching city B from city A after the construction of the highway.
Question 28 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19ba5273b2305849799e7.png' />
If in the figure, PA, QB, RC and SD are all perpendiculars to a line l, AB = 6 cm, BC = 9 cm, CD = 12 cm and SP = 36 cm. Find RS.
Question 29 :
It is given that $\Delta$ABC ~ $\Delta$PQR,with $\frac{BC}{QR}=\frac{1}{3}$. Then,$\frac{area\ of\ PRQ}{area\ of\ BCA}$ is equal to
Question 30 :
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 find out if $\frac{OA}{OC}$ =$\frac{OB}{OD}$ ?
Question 32 :
Areas of two similar triangles are 36 $cm^2$and 100 $cm^2$. If the length of a side of the larger triangle is 20 cm, find the length of the corresponding side of the smaller triangle.
Question 33 :
A flag pole 18 m high casts a shadow 9.6 m long. Find the distance of the top of the pole from the far end of the shadow.
Question 34 :
CD and GH are respectively the bisectors of ∠ACB and ∠ EGF such that D and H lie on sides AB and FE of ∆ ABC and ∆ EFG respectively. If ∆ABC ~ ∆ FEG, is $\frac{AC}{CD}$ = $\frac{GH}{FG}$ ?
Question 35 :
State True or False: A and B are respectively the points on the sides PQ and PR of a triangle PQR such that PQ = 12.5 cm, PA = 5 cm, BR= 6 cm and PB = 4 cm. Then AB is parallel to QR.
Question 37 :
If corresponding angles of two triangles are equal, then they are known as ___________ triangles.
Question 38 :
An aeroplane leaves an Airport and flies due North at 300 km/h. At the same time, another aeroplane leaves the same Airport and flies due West at 400 km/h. How far apart the two aeroplanes would be after 1 hour and 30 minutes?
Question 39 :
In a quadrilateral ABCD, $\angle$A + $\angle$D = 90°. Then it can be said that,
Question 40 :
A street light bulb is fixed on a pole 6 m above the level of the street. If a woman of height 1.5 m casts a shadow of 3 m, find how far she is away from the base of the pole.
Question 41 :
If a line is drawn parallel to one side of a triangle to intersect the other two sides, then the two sides are divided in the same ratio.
Question 42 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c6f273b230584979ada.PNG' />
In the above fig, ABC is a triangle in which ∠ABC > 90° and AD ⊥ CB produced. Is $AC^2$ = $AB^2 + BC^2 + 2 BC . BD$ ?
Question 43 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c54273b230584979ab9.PNG' />
In the above fig (i) and (ii), DE || BC. Find AD in (ii).
Question 44 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c46273b230584979aa9.PNG' />
Are the two triangles given in the fig above similar ?
Question 45 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19ba8273b2305849799eb.png' />
In the above figure, if O is the point of intersection of two chords AB and CD such that OB = OD, then triangles OAC and ODB are
Question 46 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c63273b230584979acb.PNG' />
In the above fig, altitudes AD and CE of ∆ ABC intersect each other at the point P. Is ∆ PDC ~ ∆ CEB ?
Question 47 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c6d273b230584979ad7.PNG' />
In the above fig, the perpendicular from A on side BC of a ∆ ABC intersects BC at D such that DB = 3 CD. Is $2AB^2$ = $2AC^2 + BC^2$ ?
Question 48 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b9c273b2305849799db.png' />
From the above given figure, find the value of x for which DE is parallel of AB.
Question 49 :
Two sides of triangles are given below. Determine the length of their hypotenuse. (i) 7 cm, 24 cm ; (ii)12 cm, 5 cm.
Question 50 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c6b273b230584979ad5.PNG' />
In the above fig, O is a point in the interior of a triangle ABC, OD ⊥ BC, OE ⊥AC and OF ⊥AB. Is $OA^2 + OB^2 + OC^2 – OD^2 – OE^2 – OF^2$ = $AF^2 + BD^2 + CE^2$ ?
