In $\triangle\text{ABC, BC = AB}$ and $\angle\text{B}=80^{\circ}.$ Then, $\angle\text{A = ?}$
View full solution →- 50°
- 40°
- 100°
- 80°
Question types
Congruence of Triangles and Inequalities in a Triangle question types
76 questions across 7 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
76
Questions
7
Question groups
5
Question types
01
M.C.Q
18 Q→02Fill In The Blanks[1 Marks ]
9 Q→031 Marks Question
5 Q→042 Marks Questions
5 Q→053 Marks Question
11 Q→064 Marks Questions
6 Q→075 Marks Questions
22 Q→Sample Questions
Congruence of Triangles and Inequalities in a Triangle questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
In $\triangle\text{ABC}$ and $\triangle\text{DEF,}$ it is given that $\angle\text{B}=\angle\text{E}$ and $\angle\text{C}=\angle\text{F}.$ In order that $\triangle\text{ABC}\cong\triangle\text{DEF},$ we must have:
View full solution →- AB = DF
- AC = DE
- BC = EF
- $\angle\text{A}=\angle\text{D}$
If the altitudes from two vertices of a triangle to the opposite sides are equal, then the triangle is:
- Equilateral
- Isosceles
- Scalene
- Right-angled
In $\triangle\text{ABC,}$ if $\angle\text{C}>\angle\text{B},$ then:
View full solution →- BC > AC
- AB > AC
- AB < AC
- BC < AC
In $\triangle\text{ABC}$ and $\triangle\text{DEF,}$ it is given that AB = DE and BC = EF. In order that $\triangle\text{ABC}\cong\triangle\text{DEF},$ we must have:
View full solution →- $\angle\text{A}=\angle\text{D}$
- $\angle\text{B}=\angle\text{E}$
- $\angle\text{C}=\angle\text{F}$
- none of these
(Sum of three altitudes of a triangle) (sum of its three side).
Medians of an equilateral triangle are .
Drawing a $\triangle\text{ABC}$ with AB = 3cm, BC = 4cm and CA = 7cm is .
View full solution →(Perimenter of a triangle) (sum of its three medians)
In a right triangle the hypotenuse is the side.
Is it possible to construct a triangle with lengths of its sides as given below? Give reason for your answer.
3cm, 4cm, 8cm
3cm, 4cm, 8cm
Is it possible to construct a triangle with lengths of its sides as given below? Give reason for your answer.
5cm, 4cm, 9cm
5cm, 4cm, 9cm
Is it possible to construct a triangle with lengths of its sides as given below? Give reason for your answer.
2.5cm, 5cm, 7cm
2.5cm, 5cm, 7cm
Is it possible to construct a triangle with lengths of its sides as given below? Give reason for your answer.
10cm, 5cm, 6cm
10cm, 5cm, 6cm
Is it possible to construct a triangle with lengths of its sides as given below? Give reason for your answer.
8cm, 7cm, 4cm
8cm, 7cm, 4cm
In $\triangle\text{ABC, }\angle\text {A}=100^{\circ}$and $\angle\text{C}=50^{\circ}.$ Which is its shortest side?
View full solution →In $\triangle\text{ABC, }\angle\text {A}=90^{\circ}.$ Which is its longest side?
View full solution →In $\triangle\text{ABC, }\angle\text {A}= \angle\text{B}=45^{\circ}.$ Which is its longest side?
View full solution →“If two sides and an angle of one triangle are equal to two sides and an angle of another triangle then the two triangles must be congruent.” Is the statement true? Why?
“If two angles and a side of one triangle are equal to two angles and a side of another triangle then the two triangles must be congruent.” Is the statement true? Why?
In the given figure, AD and BC are equal perpendiculars to a line segment AB.
Show that CD bisects AB.
Show that CD bisects AB.
The bisectors of $\angle\text{B}$ and $\angle\text{C}$ of an isosceles triangle with AB = AC intersect each other at a point O. BO is produced to meet AC at a point M. Prove that $\angle\text{MOC}=\angle\text{ABC}.$
View full solution →In the given figure, PQ > PR and QS and RS are the bisectors of $\angle\text{Q}$ and $\angle\text{R}$ respectively. Show that SQ > SR.
View full solution →In the given figure, two parallel line l and m are intersected by two parallel lines p and q.
Show that $\triangle\text{ABC}\cong\triangle\text{CDA}.$
View full solution →Show that $\triangle\text{ABC}\cong\triangle\text{CDA}.$
In $\triangle\text{ABC},\angle\text{A}=50^{\circ}$ and $\angle\text{B}=60^{\circ}$ Determine the longest and shortest sides of the triangle.
View full solution →D is any point on the side AC of $\triangle\text{ABC}$ with AB = AC. Show that CD < BD.
View full solution →In the adjoining figure, explain how one can find the breadth of the river without crossing it.
In a $\triangle\text{ABC, D}$ is the midpoint of side AC such that $\text{BD}=\frac{1}{2}\text{AC}.$ Show that $\angle\text{ABC}$ is a right angle.
View full solution →P is a point on the bisector of $\angle\text{ABC}.$ If the line through P, parallel to BA meets BC at Q, prove that $\triangle\text{BPQ}$ is an isosceles triangle.
View full solution →The bisectors of $\angle\text{B}$ and $\angle\text{C}$ of an isosceles $\triangle\text{ABC}$ with AB = AC intersect each other at a point O.Show that the exterior angle adjacent to $\angle\text{ABC}$ is equal to $\angle\text{BOC}.$
View full solution →In a quadrilateral ABCD, show that (AB + BC + CD + DA) > (AC + BD).
Prove that in a triangle, other than an equilateral triangle, angle opposite the longest side is greater than $\frac{2}{3}$ of a right angle.
View full solution →In the given figure, O is a point in the interior of square ABCD such that $\triangle\text{OAB}$ is an equilateral triangle. Show that $\triangle\text{OCD}$ is an isosceles triangle.
View full solution →In the given figure, $\text{AD}\perp\text{BC}$ and CD > BD. Show that AC > AB.
View full solution →In the given figure, OA = OB and OP = OQ. Prove that (i) PX = QX, (ii) AX = BX.
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