Question 1 :
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 2 :
<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 3 :
If a line divides any two sides of a triangle in the same ratio, then the line is ___________ to the third side.
Question 4 :
State True or False: In a $\Delta$ PQR, $PR^2-PQ^2=QR^2$ and M is a point on side PR such that QM is perpendicular to PR. Then $QM^2=PM.MR$.
Question 5 :
<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 6 :
<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 7 :
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 8 :
State true or false:
If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.
Question 9 :
O is the point of intersection of the diagonals AC and BD of a trapezium ABCD with AB is parallel to DC. Through O, a line segment PQ is drawn parallel to AB meeting AD in P and BC in Q. Then PO = QO.
Question 10 :
<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 11 :
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 12 :
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 13 :
<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 14 :
<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 15 :
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 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 ∆ DCB ~ ∆ HGE ?
Question 17 :
State True or False: The triangle with sides 25 cm, 5 cm and 24 cm is a right triangle.
Question 18 :
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 19 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c41273b230584979aa3.PNG' />
Are the two figures shown above similar ?
Question 20 :
Two sides of triangles are given below. Determine the length of their hypotenuse. (i) 7 cm, 24 cm ; (ii)12 cm, 5 cm.