Triangles. 3.In the following fig. AB = AC and BD = DC, then ADC = (A) 60 (B) 120 (C) 90 (D) none 4.In the Fig. given below, find Z.


 Hugh Clifford Miller
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1 Triangles <1M> 1.Two sides of a triangle are 7 cm and 10 cm. Which of the following length can be the length of the third side? (A) 19 cm. (B) 17 cm. (C) 23 cm. of these. 2.Can 80, 75 and 20 form a triangle? (A) Yes (B) Sometimes (C) No 3.In the following fig. AB = AC and BD = DC, then ADC = (A) 60 (B) 120 (C) 90 (D) none 4.In the Fig. given below, find Z. (A) 20 (B) 110 (C) 45 5.In a right angled triangle, the square of the hypotenuse is equal to twice the product of the other two sides. One of the acute angles of the triangle is (A) 60 (B) 45 (C) 30 (D) 75 6.The interior opposite angles of the exterior angle ACD are (A) B, C (B) A, C (C) A, B (D) B, E 7.If P is a point equidistant from two lines l and m intersecting at point A. Show that the line AP bisects the angle. (A) opposite side
2 (B) one side (C) between 8.Which of the following statement is correct? (A) The difference of any two sides is greater than the third side. (B) A triangle can have two obtuse angles. (C) A triangle can have an obtuse angle and a right angle.. 9.If a, b and c are the sides of a triangle, then (A) a  b > c (B) c > a + b (C) c = a + b (D) b < c + a 10.In ABC, AD BC, B= C and AB = AC. State by which property ADB ADC? (A) SAS property (B) SSS property (C) RHS property (D) ASA property 11.Two sides of a triangle are 7 cm and 10 cm. Which of the following length can be the length of the third side? (A) 19 cm (B) 17 cm (C) 23 cm of these 12.If two triangles have their corresponding angles equal, then they are not always congruent. (A) True (B) False (C) Cannot be determined.. 13.Angles opposite to equal sides of an triangle are equal. This result can be proved in many ways. One of the proofs is given here. (A) Right angle (B) isosceles (C) a & b both 14.In the given figure it is given that AB = CF, EF = BD and AFE = DBC.Then AFE congruent to CBD by which criterion? (A) AAA (B) SSS (C) ASA 15.Can 7 cm, 8 cm and 11 cm form a triangle? (A) Yes (B) No (C) Sometimes. (D) Can't say. 16.In the following, the set of measures which can not form a triangle are (A) 70, 90, 20
3 (B) 65, 75, 40 (C) 65, 85, 30 (D) 45, 45, In a ABC if then A, B, C are (A) 30, 60, 90 (B) 60, 36, 20 (C) 30, 90, 60 (D) none of these. 18.Two figures are congruent, if they are of the (A) same shape. (B) same size. (C) a & b both.. 19.In the given fig., if AD = BC and AD BC, then (A) AB = AD (B) AB = DC (C) BC = CD (D) none 20.In ABC, AB = AC and AD is perpendicular to BC. State the property by which ADB ADC. (A) SAS property (B) SSS property (C) RHS property 21.By which congruency property, the two triangles connected by the following figure are congruent. (A) SSA property (B) SSS property (C) AAS property (D) ASA property 22.A, B, C are the three angles of a triangle. If A  B = 35, B  C = 43 then A, B, C are (A) 80, 65, 35 (B) 65, 80, 35 (C) 35, 80, 65 of these. 23.Which of the following statements is not true? (A) Two line segments having the same length are congruent. (B) Two squares having the same side length are congruent. (C) Two circles having the same radius are congruent.. 24.E and F are respectively the midpoints of equal sides AB and AC of ABC.Which of the following statement is true? (A) AB = BC
4 (B) AE = AC (C) BF = CE (D) BC = AF 25.Body 26.In the adjoining figure AB PQ, AC PR, BC QR. Then, AP is (A) A median of (B) The angular bisector of (C) Perpendicular to QR of them 27.Which of the following statements is/are true? (A) Two triangles having same area are congruent. (B) If two sides and one angle of a triangle are equal to the corresponding two sides and the angle of another triangle, then the two triangles are congruent. (C) If the hypotenuse of one right triangle is equal to the hypotenuse of another triangle, then the triangles are congruent.. 28.In ABC, B = 45, C = 65 and the bisector of BAC meets BC at P. Then the descending order of sides is (A) AP, BP, CP (B) BC,AB,AC (C) BP, AP, CP (D) CP, BP, AP <2M> 29. In Figure OA = OB and OD = OC. Show that (i) AOD BOC (ii) AD BC. 30.ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal. Show that (i) ABE ACF (ii) AB = AC, i.e., ABC is an isosceles triangle.
5 31.AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB. <3M> 32.D is a point on side BC of ABC such that AD = AC.Show that AB > AD. 33. ABC and DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC. If AD is extended to intersect BC at P, show that (i) ABD ACD (ii) ABP ACP 34.ABC and DBC are two isosceles triangles on the same base BC. Show that ABD = ACD. 35.Angles opposite to equal sides of an isosceles triangle are equal. 36. In Fig, AC = AE, AB = AD and BAD = EAC. Show that BC = DE.
6 37. AB is a line segment and P is its midpoint. D and E are points on the same side of AB such that BAD = ABE and EPA = DPB. Show that (i) DAP EBP (ii) AD = BE 38.In ABC, the bisector AD of A is perpendicular to side BC. Show that AB = AC and ABC is isosceles. 39.P is a point equidistant from two lines l and m intersecting at point A. Show that the line AP bisects the angle between them. 40.In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD. Show that AD = AE. <5M> 41. ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. Show that BCD is a right angle. 42.AB is a linesegment. P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B. Show that the line PQ is the perpendicular bisector of AB.
7 43.If D is the midpoint of the hypotenuse AC of a right triangle ABC, prove that
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