Master Chapter 6.3 (Triangles) for your upcoming SEBA HSLC Board Exams!
Below, you’ll find easy-to-understand, step-by-step solutions for every question in SEBA Class 10 Maths Exercise 6.3, focusing on the criteria for similarity of triangles (AAA, SAS, SSS).
Q.2 In Fig. 6.38, △ODC ~ △OBA, ∠BOC = 125° and ∠CDO = 70°. Find ∠DOC, ∠DCO and ∠OAB.
Q.3 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, show that OA/OC = OB/OD.
Q.4 In Fig. 6.39, QR/QS = QT/PR and ∠1 = ∠2. Show that △PQS ~ △TQR.
Q 5. S and T are points on sides PR and QR of △PQR such that ∠P = ∠RTS. Show that △RPQ ~ △RTS.
Q.6 In Fig. 6.40, if △ABE ≅ △ACD, show that △ADE ~ △ABC.
Q.7 In Fig. 6.41, altitudes AD and CE of △ABC intersect each other at the point P. Show that:
(i) △AEP ~ △CDP
(ii) △ABD ~ △CBE
(iii) △AEP ~ △ADB
(iv) △PDC ~ △BEC
Q.8 E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that △ABE ~ △CFB.
Q.9 In Fig. 6.42, ABC and AMP are two right triangles, right angled at B and M respectively. Prove that:
(i) △ABC ~ △AMP
(ii) CA/PA = BC/MP
Solution:-
Q 10.
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, show that:
(i) CD/GH = AC/FG
(ii) △DCB ~ △HGE
(iii) △DCA ~ △HGF
Q. 11
In Fig. 6.43, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, prove that △ABD ~ △ECF.
Q 12.
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. 6.44). Show that ΔABC ~ ΔPQR.
Q 13.
D is a point on the side BC of a triangle ABC such that ∠ADC = ∠BAC. Show that CA² = CB.CD.
Q 14.
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. Show that ΔABC ~ ΔPQR.
Q 15.
A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.
Q 16.
If AD and PM are medians of triangles ABC and PQR, respectively where ΔABC ~ ΔPQR, prove that AB/PQ = AD/PM.
Q 17.
In the following figure, Q is a point on PR and S is a point on TR. QS is drawn and ∠RPT = ∠RQS (Fig. 6.45)
Fig. 6.45
Which of the following criteria can be used to prove ΔRSQ is similar to ΔRTP?
(A) AAA similarity criterion
(B) SAS similarity criterion
(C) SSS similarity criterion
(D) RHS similarity criterion
Q 18.
Assertion (A): If ΔABC and ΔPQR are congruent triangles, then they are also similar triangles.
Reason (R) : All congruent triangles are similar but similar triangles are not necessarily congruent.
(A) Both A and R are true and R is the correct explanation of A.
(B) Both A and R are true but R is not the correct explanation of A
(C) A is true but R is false
(D) A is false but R is true.
Q 19.
Assertion (A) : If ΔABC and ΔPQR are right triangles, right angled at C and R respectively such that AB/PQ = AC/PR, then ∠B = ∠Q
Reason (R) : In two right triangles if hypotenuse and one side of the triangle are proportional to the hypotenuse and one side of the other triangle, then the two triangles are similar by S-A-S similarity criterion.
A) Both A and R are true and R is the correct explanation of A.
B) Both A and R are true but R is not the correct explanation of A.
C) A is true but R is false.
D) A is false but R is true.
Q 20.
Q 21.
Master your geometry concepts with our complete SEBA Class 10 Maths guide, specifically tailored for students preparing for the Assam state board examinations. In this dedicated lesson on Chapter 6.3 Triangles, we break down every problem step-by-step so you can easily tackle Class 10 Exercise 6.3 Solutions without confusion. Designed as an all-in-one SEBA HSLC Maths Guide, this post provides comprehensive Assam Board Class 10 Solutions that focus deeply on core concepts like the Criteria for Similarity of Triangles (AAA, SAS, SSS), ensuring you score maximum marks in your upcoming board exams.
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