Question 1 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c40273b230584979aa1.PNG' />
Are the two figures shown above similar ?
Question 2 :
If S is a point on side PQ of a $\Delta$ PQR such that PS = QS = RS, then
Question 3 :
Determine which of them are right triangles:
(i) 7 cm, 24 cm, 25 cm
(ii) 3 cm, 8 cm, 6 cm
(iii) 50 cm, 80 cm, 100 cm
(iv) 13 cm, 12 cm, 5 cm
Question 5 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c5f273b230584979ac6.PNG' />
In the above fig, ∆ ODC ~ ∆ OBA, ∠ BOC = 125° and ∠ CDO = 70°. Find ∠OAB.
Question 6 : <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 7 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c4d273b230584979ab1.PNG' />
In the above fig, CM and RN are respectively the medians of ∆ ABC and ∆ PQR. If ∆ ABC ~ ∆ PQR, Is ∆ CMB ~ ∆ RNQ ?
Question 8 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c71273b230584979adc.PNG' />
In the above fig, AD is a median of a triangle ABC and AM ⊥ BC. Is $AB^2$ = $AD^2 – BC . DM + \left(\frac{BC}{2}\right)^2$ ?
Question 9 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c55273b230584979abb.PNG' />
In the above fig, DE || AC and DF || AE. Is $\frac{BF}{FE}$ = $\frac{BE}{EC}$ ?
Question 10 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c41273b230584979aa2.PNG' />
Are the two figures shown above similar ?
Question 11 :
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 ∆ DCB ~ ∆ HGE ?
Question 12 :
State true or false:
If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.
Question 13 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c74273b230584979ae0.PNG' />
In the above fig, two chords AB and CD of a circle intersect each other at the point P(when produced) outside the circle. Which of these is true :(i) ∆ PAC ~ ∆ PDB (ii) PA . PB = PC . PD
Question 14 :
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 15 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c4c273b230584979ab0.PNG' />
In the above fig, CM and RN are respectively the medians of ∆ ABC and ∆ PQR. If ∆ ABC ~ ∆ PQR, Is $\frac{CM}{RN}$ = $\frac{AB}{PQ}$ ?
Question 16 : <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 17 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c3f273b230584979aa0.PNG' />
Which of these shown in the above figure contain similar figures ?
Question 18 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c5e273b230584979ac5.PNG' />
In the above fig, ∆ ODC ~ ∆ OBA, ∠ BOC = 125° and ∠ CDO = 70°. Find ∠DCO.
Question 20 :
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 21 :
Two sides of triangles are given below. Determine the length of their hypotenuse. (i) 7 cm, 24 cm ; (ii)12 cm, 5 cm.
Question 22 :
Two polygons of the same number of sides are similar, if (a) their corresponding angles are ___________ and (b) their corresponding sides are ___________.
Question 23 :
State True or False: In triangles PQR and MST, $\angle$P = 55°, $\angle$Q = 25°, $\angle$M = 100° and $\angle$S = 25°. Then $\Delta$ QPR ~ $\Delta$ TSM.
Question 24 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c69273b230584979ad2.PNG' />
In the above fig, ABD is a triangle right angled at A and AC ⊥ BD. Is $AB^2$ = $BC . BD$ ?
Question 26 :
In an equilateral triangle, can it be proved that three times the square of one side is equal to four times the square of one of its altitudes ?
Question 27 :
State True or False:In two triangles, an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle, then the triangles are similar.
Question 28 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c6a273b230584979ad4.PNG' />
In the above fig, ABD is a triangle right angled at A and AC ⊥ BD. Is $AD^2$ = $BD . CD$ ?
Question 29 :
State True or False: Two quadrilaterals are similar, if their corresponding angles are equal.
Question 30 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c5a273b230584979ac1.PNG' />
Are the triangles shown in the above fig similar ?
