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EDU.VISTA INSTITUTE, Quality Before Quantity, , TRIANGLE -CONGRUENCY (PRACTICE SHEET-9TH), Class 09 - Mathematics, Time Allowed: 1 hour, 1., , Maximum Marks: 68, , Read the Source/Text given below and answer any four questions:, , [5], , Hareesh and Deep were trying to prove a theorem. For this they did the following;, i. Drew a triangle ABC, ii. D and E are found as the mid points of AB and AC, iii. DE was joined and DE was extended to F so DE = EF, iv. FC was joined., Answer the following questions:, i. ΔADE and ΔEFC are congruent by which criteria?, a. SSS, b. RHS, c. SAS, d. ASA, ii. ∠EFC is equal to which angle?, a. ∠DAE, b. ∠ADE, c. ∠AED, d. ∠B, iii. ∠ECF is equal to which angle?, a. ∠DAE, b. ∠ADE, c. ∠AED, d. ∠B, iv. CF is equal to which of the following?, a. BD, b. CE, 1 / 13

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c. AE, d. EF, v. CF is parallel to which of the following?, i. AE, ii. CE, iii. BD, iv. EF, 2., , Read the Source/Text given below and answer any four questions:, , [5], , In the middle of the city, there was a park ABCD in the form of a parallelogram form so that, AB=CD, AB||CD and AD = BC, AD || BC, Municipality converted this park into a rectangular form by adding land in the form of ΔAPD, and Δ BCQ. Both the triangular shape of land were covered by planting flower plants., , Answer the following questions:, i. What is the value of ∠x?, a. 110°, b. 70°, c. 90°, d. 100°, ii. ΔAPD and Δ BCQ are congruent by which criteria?, a. SSS, b. SAS, c. ASA, d. RHS, iii. PD is equal to which side?, a. DC, b. AB, c. BC, d. BQ, iv. ΔABC and ΔACD are congruent by which criteria?, a. SSS, b. SAS, c. ASA, d. RHS, v. What is the value of ∠m?, a. 110°, 2 / 13

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b. 70°, c. 90°, d. 20°, 3., , In figure, ABC is a triangle in which ∠B = 2∠C. D is a point on side BC such that AD bisects, ∠, , BAC and AB = CD. BE is the bisector of ∠B. The measure of ∠BAC is, , [Hint: ΔABE, , 4., , 5., , ≅ΔDCE, , 7., , ], , a) 74°, , b) 73°, , c) 72°, , d) 95°, , In the given figure AB > AC. If BO and CO are the bisectors of ∠B and, , a) OB = OC, , b) None of these, , c) OB < OC, , d) OB > OC, , In ΔABC, , and ΔDEF, , ΔABC ≅ΔDEF, , 6., , [1], , its is given that ∠B =, , ∠E and ∠C = ∠F, , ∠C, , respectively then, , in order that, , b), , c) AB = DF, , d) AC = DE, , ∠A = ∠D, , In the adjoining figure, AC = BD. If ∠CAB = ∠DBA, then ∠ACB is equal to, , ∠, , c), , ∠, , [1], , we must have, , a) BC = EF, , a), , [1], , ABC, , b), , ∠, , BDA, , ABD, , d), , ∠, , BAD, , In the adjoining figure, AB = AC and AD is bisector of ∠A. The rule by which, , [1], , [1], , △ABD ≅△ACD, , 3 / 13

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8., , 9., , a) SSS, , b) SAS, , c) AAS, , d) ASA, , In the adjoining figure, the rule by which △ABC, , [1], , ≅△ADC, , a) SAS, , b) SSS, , c) AAS, , d) RHS, , In quadrilateral ABCD, BM and DN are drawn perpendiculars to AC such that BM = DN. If BR =, , [1], , 8 cm. then BD is, , 10., , 11., , 12., , a) 12 cm, , b) 4 cm, , c) 16 cm, , d) 2 cm, , In the adjoining figure, ∠B = ∠C and AD⊥ BC. The rule by which △ABD ≅△ADC, , a) SSS, , b) SAS, , c) RHS, , d) AAS, , In a △ABC , if ∠A − ∠B =, , ∘, , 42, , and ∠B − ∠C, , ∘, , = 21, , a) 95o, , b) 63o, , c) 53o, , d) 32o, , [1], , then ∠B = ?, , [1], , In the given figure, two rays BD and CE intersect at a point A. The side BC of △ABC have been, produced on both sides to points F and G respectively. If ∠ABF =, ∠DAE = z, , ∘, , ∘, , x, , , ∠ACG, , = y, , ∘, , [1], , and, , then z = ?, , a) x + y - 180, , b) x + y + 180, 4 / 13

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c) 180 - (x + y), 13., , d) x + y + 360o, , In △AOC and △XYZ, ∠A =, △AOC ≅△XY Z, , 14., , , AO = XY, AC = XZ, then by which congruence rule, , ∠X, , [1], , ?, , a) SSS, , b) SAS, , c) RHS, , d) ASA, , In the given figure, lines AB and CD intersect at a point O. The sides CA and OB have been, , [1], , produced to E and F respectively such that ∠OAE = x° and ∠DBF = y°., , If ∠OCA =, , ∘, , 80, , , ∠COA =, , ∘, , 40, , and ∠BDO =, , then xo + yo = ?, , ∘, , 70, , a) 210o, , b) 190o, , c) 270o, , d) 230o, [1], , 15., , In the above figure AB ∥ CD ,O is the mid point BC. Which of the following is true?, a), , AOB ≅△DOC, , b) AB = CD, , △, , c) O is the mid point of AD, 16., , in ΔABC, , and ΔDEF, , d) All are true, , it is given that AB = DE and BC = EF in order that ΔABC, , ≅ΔDEF ,, , [1], , we must have, , 17., , 18., , a), , ∠C = ∠F, , b), , c), , ∠B = ∠E, , d) None of these, , ∠A = ∠D, , In the adjoining figure, AB = AC and AD is median of △ABC , then ∠ADC is equal to, , a), , 90, , ∘, , b), , 60, , c), , 75, , ∘, , d), , 120, , [1], , ∘, , ∘, , In the adjoining figure, AB = FC, EF = BD and ∠AFE = ∠CBD. Then the rule by which, , [1], , △AF E ≅△CBD, , 5 / 13

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19., , 20., , a) SSS, , b) AAS, , c) ASA, , d) SAS, , In the adjoining figure, AB = BC and ∠ABD = ∠CBD, then another angle which measures 30 is [1], ∘, , a), , ∠, , BCA, , b), , ∠, , BCD, , c), , ∠, , BDA, , d), , ∠, , BAD, , In figure, what is y in terms of x?, , a), , 3, 2, , x, , c) x, 21., , 22., , [1], , b), , 3, , d), , 4, , 4, , 3, , x, x, , In figure, ABCD is a quadrilateral in which AB = BC and AD = DC. The measure of ∠BCD is:, , a) 30o, , b) 105o, , c) 150o, , d) 72o, , In △ABC, BC = AB and ∠B = 80°. Then ∠A is equal to, a) 50°, , [1], , [1], , b) 40°, , 6 / 13

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c) 80°, 23., , 24., , 25., , d) 100°, , In the adjoining figure, AB⊥ BE and FE⊥ BE. If AB = FE and BC = DE ,then, , a), , △ABD ≅△EF C, , b), , △ABD ≅△CEF, , c), , △ABD ≅△ECF, , d), , △ABD ≅△F EC, , In figure, if AE||DC and AB = AC, the value of ∠ABD is, , a) 110°, , b) 120°, , c) 130°, , d) 70°, , In fig., △ABD ≅△ACD, AB = AC, BD = DC name the criteria by which the triangles are, , [1], , [1], , [1], , congruent:, , 26., , a) ASA, , b) RHS, , c) SSS, , d) SAS, , In the adjoining figure, ABCD is a quadrilateral in which AD = CB and AB = CD, then ∠ACB is, , [1], , equal to, , 27., , a), , ∠, , BAC, , b), , ∠, , BAD, , c), , ∠, , CAD, , d), , ∠, , ACD, , The sides BC, CA and AB of △ABC have been produced to D, E and F respectively., ∠BAE + ∠CBF + ∠ACD =, , [1], , ?, , 7 / 13

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28., , a) 240o, , b) 360o, , c) 300o, , d) 320o, , In the adjoining figure, △ABC, , ≅△ADC, , . If ∠BAC = 30 and ∠ABC = 100 then ∠ACD is, ∘, , ∘, , [1], , equal to, , 29., , 30., , 31., , a), , 50, , ∘, , b), , 80, , c), , 30, , ∘, , d), , 60, , ∘, , ∘, , In the adjoining fig. AB = AC. If ∠C = 50∘ , then the value of x and y are:, , a) x = 80o and y = 50o, , b) x = 70o and y = 60o, , c) x = 50o and y = 80o, , d) x = 60o and y = 70o, , In figure, what is the value of x?, , [1], , [1], , a) 60, , b) 35, , c) 45, , d) 50, , If the bisector of the angle A of a △ABC is perpendicular to the base BC of the triangle then the [1], triangle ABC is:, a) Isosceles, , b) Obtuse Angled, , c) Equilateral, , d) Scalene, , 8 / 13

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32., , If the altitudes from two vertices of a triangle to the opposite sides are equal then the triangle, , [1], , is, , 33., , a) equilatera, , b) scalene, , c) right angled, , d) isosceles, , D, E and F are the mid points of sides AB, BC and CA of ΔABC . If perimetre of ΔABC is 16, , [1], , cm, then perimetre of ΔDEF ., , 34., , 35., , 36., , b) 8 cm, , c) NONE OF THESE, , d) 4 cm, , △ABC ≅△P QR, , , then which of the following is true?, , a) CA = RP, , b) CB = QP, , c) AB = RP, , d) AC = RQ, , [1], , In fig, AC = BC and ∠ACY = 140∘ . Find X and Y:, , a), , 80, , c), , 95, , [1], , ∘, , and 80, , ∘, , b), , 110, , ∘, , and 105, , d), , 50, , ∘, , ∘, , ∘, , and 110, , ∘, , and 120, , ∘, , Side BC of △ABC has been produced to D on left and to E on right-hand side of BC such that, ∠, , 37., , a) 32 cm, , [1], , ABD = 125° and ∠ACE = 130°. Then, ∠A = ?, , a) 75o, , b) 50o, , c) 65o, , d) 55o, , In △RST (See Figure), what is the value of x?, , [1], , 9 / 13

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38., , 39., , a) 100°, , b) 40°, , c) 90°, , d) 80°, , If a,b,c are the lengths of the sides of a triangle, then, , [1], , a) C < A + B, , b) C > A + B, , c) C = A + B, , d) A – B > C, , Side BC of a triangle ABC has been produced to a point D such that ∠ACD = 120°. If ∠B =, , 1, 2, , ∠, , A, [1], , then ∠A is equal to, , 40., , a) 60°, , b) 90°, , c) 80°, , d) 75°, , The area of a right angled triangle is 20 m2 and one of the sides containing the right triangle is [1], 4 cm. Then the altitude on the hypotenuse is, a) 10 cm, c), , 41., , 42., , 43., , 20, , cm, , √29, , b), , 10, , cm, , √41, , d) 8 cm, [1], , In figure, AB = AC and ∠ACD = 115o. Find ∠A ?, , a) None of these, , b) 50, , c), , d), , ∘, , 115, , 0, , ∘, , 60, , In the given figure, ABC is an equilateral triangle. The value of x + y is, , a), , 200, , ∘, , b), , 240, , c), , 120, , ∘, , d), , 180, , [1], , ∘, , ∘, , Which of the following is not a criterion for congruence of triangles?, a) ASA, , b) SAS, , c) SSA, , d) SSS, , [1], , 10 / 13

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44., , If triangle PQR is right angled at Q, then, , [1], , a) PR > PQ, , b) PR < QR, , c) PR = PQ, , d) PR < PQ, [1], , 45., In the above quadrilateral ACBD, we have AC = AD and AB bisect the ∠A .Which of the, following is true?, a), , ABC ≅△ABD, , b), , △, , c) All are true, 46., , C = ∠D, , d) BC = BD, , In triangles ABC and PQR three equality relations between some parts are as follows: AB = QP,, ∠B, , 47., , ∠, , [1], , = ∠P , BC = PR. State which of the congruence conditions applies:, , a) SSS, , b) AAS, , c) SAS, , d) ASA, , In △ABC and △PQR, AB = PR and ∠A = ∠P . Then, the two triangles will be congruent by SAS [1], axiom if:, , 48., , 49., , a) BC = QR, , b) BC = PQ, , c) AC = PQ, , d) AC = QR, , If △P QR ≡, , , then ∠E, , △EF D, , [1], , =, , a) None of these, , b), , ∠P, , c), , d), , ∠R, , ∠Q, , If △ABC≅△ PQR and △ ABC is not congruent to △ RPQ, then which of the following is not, , [1], , true:, , 50., , a) AC = PR, , b) BC = PQ, , c) AB = PQ, , d) QR = BC, , In △ABC, if ∠A = 45o and ∠B = 70o, then the shortest and the longest sides of the triangle are, , [1], , ________., , 51., , 52., , a) BC, AB, , b) AB, BC, , c) BC, AC, , d) AB, AC, , Which of the following is not possible in case of triangle ABC?, a) AB = 5cm, BC = 8cm, CA = 7cm., , b) AB = 2 cm, BC = 4 cm, CA = 7 cm., , c), , d) AB = 3cm, BC = 4cm, CA = 5cm., , ∠, , A = 50∘ , ∠B = 60∘ , ∠C = 70∘, , In the adjoining figure, BC = AD, CA⊥ AB and BD⊥ AB. The rule by which △ABC, , [1], , ≅△BAD, , [1], , is, , 11 / 13

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53., , a) ASA, , b) RHS, , c) SSS, , d) SAS, , In figure, X is a point in the interior of square ABCD. AXYZ is also a square. If DY = 3 cm and, , [1], , AZ = 2 cm, then BY =, , 54., , 55., , a) 6 cm, , b) 5 cm, , c) 8 cm, , d) 7 cm, , In the adjoining figure, PQ = PR. If ∠Q = 70 , then measure of ∠P is, ∘, , a), , 40, , c), , 110, , ∘, , ∘, , b), , 70, , d), , 80, , [1], , ∘, , ∘, , In a triangle, an exterior angle at a vertex is 95° and its one of the interior opposite angle is, , [1], , 55°, then the measure of the other interior angle is, , 56., , 57., , a) 85°, , b) 55°, , c) 90°, , d) 40°, , In the adjoining Figure, AB = AC and BD = CD. The ratio ∠ABD : ∠ACD is, , a) 1 : 1, , b) 1 : 2, , c) 2 : 3, , d) 2 : 1, , In an isosceles, △ABC AB = AC and side BA is produced to D such that AB=AD. Then the, , [1], , [1], , measure of ∠BCD is, , 12 / 13

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58., , 59., , 60., , a) 70o, , b) 90o, , c) 100o, , d) 60o, , In fig, in △ABC , AB = AC, then the value of x is:, , a) 120o, , b) 100o, , c) 130o, , d) 80o, , In the adjoining figure, if AC = AD, then, , [1], , [1], , a) AB ≤ AD, , b) AB = AD, , c) AB < AD, , d) AB > AD, , In figure, the value of x is, , [1], , a) 120°, , b) 65°, , c) 80°, , d) 95°, , 13 / 13