Question 1 :
D is a point on the side BC of a triangle ABC such that ∠ADC = ∠ BAC. Is $CA^2= CB.CD$ true ?
Question 2 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c4f273b230584979ab3.PNG' />
In the above fig, ∠ ACB = 90° and CD ⊥ AB. Is $\frac{BC^2}{AC^2} = \frac{BD}{AD}$ ?
Question 3 :
State true or false:
If in two triangles, sides of one triangle are proportional to (i.e., in the same ratio of ) the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similiar.
Question 4 :
Find the altitude of an equilateral triangle of side 8 cm.
Question 5 :
D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C.Is $AE^2 + BD^2$ = $AB^2 + DE^2$ ?
Question 6 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c60273b230584979ac8.PNG' />
In the above fig, if ∆ ABE ≅ ∆ ACD, find out if ∆ ADE ~ ∆ ABC.
Question 7 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c6e273b230584979ad8.PNG' />
In the above fig, PS is the bisector of ∠ QPR of ∆ PQR. Is $\frac{QS}{SR}$ = $\frac{PQ}{PR}$ ?
Question 8 :
State True or False: The ratio of the corresponding altitudes of two similar triangles is $\frac{3}{5}$.Then it is correct to say that ratio of their areas is
$\frac{6}{5}$.
Question 9 :
ABC is an isosceles triangle right angled at C. Is$ AB^2$ = $2AC^2$ ?
Question 10 :
An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1.5 hours?
Question 11 :
If AD and PM are medians of triangles ABC and PQR, respectively where ∆ ABC ~ ∆ PQR, Is $\frac{AB}{PQ}$ = $\frac{AD}{PM}$ ?
Question 12 :
State True or False: P and Q are the points on the sides DE and DF of a triangle DEF such that DP = 5 cm, DE = 15 cm, DQ= 6 cm and QF = 18 cm. Then PQ is parallel to EF.
Question 13 :
State True or False: The triangle with sides 25 cm, 5 cm and 24 cm is a right triangle.
Question 14 :
ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is ________ .
Question 15 : <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 16 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c72273b230584979add.PNG' />
In the above fig, AD is a median of a triangle ABC and AM ⊥ BC. Is $AC^2 + AB^2$ = $2AD^2 + \frac{1}{2} BC^{2}$?
Question 17 :
State True or False: It is given that $\Delta$ FED ~ $\Delta$ STU. Then $\frac{DE}{ST}=\frac{EF}{TU}$.
Question 18 :
A 15 metres high tower casts a shadow 24 metres long at a certain time and at the same time, a telephone pole casts a shadow 16 metres long. Find the height of the telephone pole.
Question 19 :
If a line divides any two sides of a triangle in the same ratio, then the line is ___________ to the third side.
Question 20 : <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 21 :
Hypotenuse of a right triangle is 25 cm and out of the remaining two sides, one is longer than the other by 5 cm. Find the lengths of the other two sides.
Question 22 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c53273b230584979ab8.PNG' />
In the above fig, (i) and (ii), DE || BC. Find EC in (i).
Question 23 :
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 24 :
I - All congruent figures are similar.
II - All similar figures are congruent.
Which of these is correct ?
Question 25 :
State True or False: D is a point on side QR of $\Delta$PQR such that PD is perpendicular to QR. Then it is correct to say that $\Delta$PQD ~ $\Delta$RPD ?
Question 26 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c55273b230584979aba.PNG' />
In the above fig, if LM || CB and LN || CD, Is $\frac{AM}{AB}$ = $\frac{AN}{AD}$ ?
Question 29 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c73273b230584979adf.PNG' />
In the above fig, two chords AB and CD intersect each other at the point P. Which of these is true : (i) ∆APC ~ ∆ DPB (ii) AP . PB = CP . DP
Question 30 :
If $\Delta$ABC ~ $\Delta$EDF and $\Delta$ ABC is not similar to $\Delta$DEF, then which of
the following is not true?
Question 31 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c5a273b230584979ac0.PNG' />
Are the triangles shown in the above fig similar ?
Question 32 :
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 __________ ratio.
Question 33 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c65273b230584979ace.PNG' />
In the above fig, ABC and AMP are two right triangles, right angled at B and M respectively. Is ∆ABC ~ ∆AMP ?
Question 34 :
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 35 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19ba6273b2305849799e9.png' />
State True or False: In the above figure, OB is the perpendicular bisector of the line segment DE, FA is perpendicular to OB and FE intersects OB at the point C. Then we can say that $\frac{1}{OA}+\frac{1}{OB}=\frac{1}{OC}$
Question 36 :
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 37 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c76273b230584979ae2.PNG' />
In the above fig, D is a point on side BC of ∆ ABC such that $\frac{BD}{CD}$ = $\frac{AB}{AC}$⋅ Is AD the bisector of ∠ BAC ?
Question 38 :
Two polygons of the same number of sides are similar, if (a) their corresponding angles are ___________ and (b) their corresponding sides are ___________.
Question 39 :
Let ∆ ABC ~ ∆ DEF and their areas be, respectively, 64 $cm^2$ and 121 $cm^2$ . If EF = 15.4 cm, find BC.
Question 40 :
State True or False: Two quadrilaterals are similar, if their corresponding angles are equal.
Question 42 :
If S is a point on side PQ of a $\Delta$ PQR such that PS = QS = RS, then
Question 43 :
Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.
Question 44 :
State True or False: Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Then the two triangles will be similar.
Question 45 : <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 46 :
If in $\Delta$ABC and $\Delta$DEF, $\frac{AB}{DE}=\frac{BC}{FD}$ then they will be similar, when
Question 48 :
Foot of a 10 m long ladder leaning against a vertical wall is 6 m away from the base of the wall. Find the height of the point on the wall where the top of the ladder reaches.
Question 49 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b9e273b2305849799de.png' />
In the given figure, if $\angle$ ACB = $\angle$ CDA, AC= 8 cm and AD = 3 cm, Find BD.
Question 50 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b9b273b2305849799da.png' />
In the above figure, if $\angle$1=$\angle$2 and $\Delta$ NSQ is congruent to $\Delta$ MTR, then $\Delta$ PTS is similar to $\Delta$ PRQ.
