Use the information in the given figure to prove:$(i) \mathrm{AB}=\mathrm{FE}\ (ii) \ \mathrm{BD}=\mathrm{CF}$
View full solution →Question types
Triangles [Congruency in Triangles] question types
61 questions across 4 question groups — pick any mix to generate a MATHEMATICS paper with step-by-step answer keys.
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Sample Questions
Triangles [Congruency in Triangles] questions
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In the following figure$, A B=A C$ and $A D$ is perpendicular to $B C$. $B E$ bisects angle $B$ and $E F$ is perpendicular to $A B$. Prove that$: \mathrm{ED}=\mathrm{EF}$
View full solution →In the following figure $, A B=A C$ and $A D$ is perpendicular to $B C$. $B E$ bisects angle $B$ and $E F$ is perpendicular to $A B.$ Prove that $: \mathrm{BD}=\mathrm{CD}$
View full solution →In the following figure $, \mathrm{BL}=\mathrm{CM}.$
Prove that $AD$ is a median of triangle $ABC$.
View full solution →Prove that $AD$ is a median of triangle $ABC$.
In the following figure, $\text{AB}=\text{EF},\text{BC}=\text{DE}$ and $\angle B=\angle E=90^{\circ}$.
Prove that $\text{AD}=\text{FC}$
View full solution →Prove that $\text{AD}=\text{FC}$
$\text{AD}$ and $\text{BC}$ are equal perpendiculars to a line segment $\text{AB}$. If $\text{AD}$ and $\text{BC}$ are on different sides of $\text{AB}$ prove that $\text{CD}$ bisects $\text{AB}.$
View full solution →If the following pair of the triangle is congruent? state the condition of congruency:In $\triangle ABC$ and $\triangle PQR, \text{AB} = \text{PQ}, \text{AB} = \text{PQ},$ and $\text{BC} = \text{QR}.$
View full solution →If the following pair of the triangle is congruent? state the condition of congruency:In $\triangle ABC$ and $\triangle QRP, \text{AB} = \text{QR}, \angle B = \angle R$ and $\angle C = P.$
View full solution →In $\triangle ABC,\text{AB} = \text{AC}.$ Show that the altitude $\text{AD}$ is median also.
View full solution →In the following diagram, $\mathrm{AP}$ and $\mathrm{BQ}$ are equal and parallel to each other.
Prove that$:(i) \triangle \mathrm{AOP} \cong \triangle \mathrm{BOQ}.(ii) \mathrm{AB}$ and $\mathrm{PQ}$ bisect each other.
View full solution →Prove that$:(i) \triangle \mathrm{AOP} \cong \triangle \mathrm{BOQ}.(ii) \mathrm{AB}$ and $\mathrm{PQ}$ bisect each other.
In the following figures, the sides $A B$ and $B C$ and the median $A D$ of $\triangle A B C$ are equal to the sides $P Q$ and $Q R$ and median $P S$ of the $\triangle P Q R$.Prove that $\triangle A B C$ and $\triangle P Q R$ are congruent.
View full solution →In the parallelogram $\text{ABCD},$ the angles $A$ and $C$ are obtuse. Points $X$ and $Y$ are taken on the diagonal $BD$ such that the angles $XAD$ and $YCB$ are right angles.Prove that: $XA = YC.$
View full solution →In a $\triangle ABC, BD$ is the median to the side $AC, BD$ is produced to $E$ such that $BD = DE.$Prove that: $AE$ is parallel to $BC$.
View full solution →In quadrilateral $\text{ABCD, AD = BC}$ and $\ce{BD = CA}.$ Prove that: $(i)\angle ADB =\angle BCA$ $(ii)\angle DAB =\angle CBA$
View full solution →$\text{ABCD}$ is a parallelogram. The sides $AB$ and $AD$ are produced to $E$ and $F$ respectively, such produced to $E$ and $F$ respectively, such that $AB = BE$ and $AD = DF$.Prove that: $\triangle BEC \cong \triangle DCF.$
View full solution →In the adjoining figure, $\mathrm{OX}$ and $\mathrm{RX}$ are the bisectors of the angles $Q$ and $R$ respectively of the triangle $P Q R$.If $X S \perp Q R$ and $X T \perp P Q$;
prove that: $(i) \triangle \mathrm{XTQ} \cong \triangle \mathrm{XSQ}.(ii) \mathrm{PX}$ bisects angle $\mathrm{P}$
View full solution →prove that: $(i) \triangle \mathrm{XTQ} \cong \triangle \mathrm{XSQ}.(ii) \mathrm{PX}$ bisects angle $\mathrm{P}$
In the figure, given below, $\triangle \mathrm{ABC}$ is right$-$angled at $\mathrm{B} . \mathrm{ABP}$ and $\text{ACRS}$ are squares.
Prove that:$(i) \triangle \mathrm{ACQ}$ and $\triangle \mathrm{ASB}$ are congruent.$(ii) \mathrm{CQ}=\mathrm{BS}$.
View full solution →Prove that:$(i) \triangle \mathrm{ACQ}$ and $\triangle \mathrm{ASB}$ are congruent.$(ii) \mathrm{CQ}=\mathrm{BS}$.
In the following diagram, $\text{ABCD}$ is a square and $\text{APB}$ is an equilateral triangle.
$(i)$ Prove that: $\triangle \mathrm{APD} \cong \triangle \mathrm{BPC}$
$(ii)$ Find the angles of $\triangle \mathrm{DPC}$.
View full solution →$(i)$ Prove that: $\triangle \mathrm{APD} \cong \triangle \mathrm{BPC}$
$(ii)$ Find the angles of $\triangle \mathrm{DPC}$.
In the following diagram, $\text{ABCD}$ is a square and $\text{APB}$ is an equilateral triangle.
$(i)$ Prove that: $\triangle \mathrm{APD} \cong \triangle \mathrm{BPC},(ii)$ Find the angles of $\triangle \mathrm{DPC}$.
View full solution →$(i)$ Prove that: $\triangle \mathrm{APD} \cong \triangle \mathrm{BPC},(ii)$ Find the angles of $\triangle \mathrm{DPC}$.
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