Download Triangles 1.Two sides of a triangle are 7 cm and 10 cm. Which

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.
(D) None of these.
2.Can 80°, 75° and 20° form a triangle?
(A) Yes
(B) Sometimes
(C) No
(D) None
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°
(D) None
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
(B) one side
(C) between
(D) None
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.
(D) None.
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
(D) None 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.
(D) None.
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
(D) None
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
(D) None
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°
(B) 65°, 75°, 40°
(C) 65°, 85°, 30°
(D) 45°, 45°, 80°
17.In a ABC if
(A) 30°, 60°, 90°
(B) 60°, 36°, 20°
then
A,
B,
C are
(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.
(D) None.
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
(D) None
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°
(D) None 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.
(D) None.
24.E and F are respectively the mid-points of equal sides AB and AC of ABC.Which of the following
statement is true?
(A) AB = BC
(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
(D) None 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.
(D) None.
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.
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
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.
ABD =
ACD.
37.
AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that
ABE and EPA = DPB. Show that
(i) DAP
EBP
(ii) AD = BE
38.In ABC, the bisector AD of
isosceles.
A is perpendicular to side BC. Show that AB = AC and
BAD =
ABC is
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 line-segment. 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.
43.If D is the mid-point of the hypotenuse AC of a right triangle ABC, prove that