In the figure $,\text{AB} =\text{EF}, \text{BC} = \text{DE}, \text{AB}$ and $\text{FE}$ are perpendiculars on $\text{BE}.$ Prove that $\triangle ABD ≅ \triangle FEC$
View full solution →Question types
Triangles and their congruency question types
51 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 and their congruency questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
In the figure, $BC = CE$ and $\angle 1 = \angle 2.$ Prove that $\triangle GCB ≅ \triangle DCE.$
View full solution → In the figure, $\angle CPD = \angle BPD$ and $AD$ is the bisector of $\angle BAC.$ Prove that $\triangle CAP ≅ \triangle BAP$ and $CP = BP.$
View full solution → In $\triangle ABC$ and $\triangle PQR$ and, $AB = PQ, BC = QR$ and $CB$ and $RQ$ are extended to $X$ and $Y$ respectively and $\angle ABX = \angle PQY. =$ Prove that $\triangle ABC ≅ \triangle PQR.$
View full solution →In $\triangle ABC, AD$ is a median. The perpendiculars from $B$ and $C$ meet the line $AD$ produced at $X$ and $Y$. Prove that $BX = CY.$
View full solution →In $\triangle ABC, AB = AC, BM$ and $Cn$ are perpendiculars on $AC$ and $AB$ respectively. Prove that $BM = CN.$
View full solution →In a circle with center $O$. If $OM$ is perpendicular to $PQ$, prove that $PM = QM.$
View full solution → $\text{PQRS}$ is a quadrilateral and $T$ and $U$ are points on $PS$ and $RS$ respectively such that $PQ = RQ, ∠PQT = ∠RQU$and $∠TQS = ∠UQS$. Prove that $QT = QU.$
View full solution →Two right$-$angled triangles $ABC$ and $ADC$ have the same base $AC$. If $BC = DC$, prove that $AC$ bisects $\angle BCD.$
View full solution →$\triangle ABC$ is an isosceles triangle with A$B = AC. GB$ and $HC ARE$ perpendiculars drawn on $BC.$
Prove that
$(i) BG = CH$
$(ii) AG = AH$
View full solution →Prove that
$(i) BG = CH$
$(ii) AG = AH$
$O$ is any point in the $\triangle ABC$ such that the perpendicular drawn from $O$ on $AB$ and $AC$ are equal. Prove that $OA$ is the bisector of $\angle BAC.$
View full solution →In $\triangle ABC, AB = AC$ and the bisectors of angles $B$ and $C$ intersect at point $O$.Prove that $BO = CO$ and the ray $AO$ is the bisector of $\angle BAC.$
View full solution → In a $\triangle ABC$, if $D$ is midpoint of $BC; AD$ is produced upto $E$ such as $DE = AD$, then prove that:$a. \text{DABD}$ and $\text{DECD}$ are congruent.$b. AB = EC,c. AB$ is parallel to $EC$
View full solution →In the given figure, $AB = DB$ and $AC = DC.$ Find the values of $x$ and $y.$
View full solution →In the given figure $P$ is a midpoint of chord $AB$ of the circle $O$. prove that $OP \perp AB.$
View full solution → In the given figure $\text{ABCD}$ is a parallelogram, $AB$ is Produced to $L$ and $E$ is a midpoint of $BC$. Show that:
$a. \text{DDCE} \cong \text{DLDE};b. A B=B L;c. DC =\frac{ AL }{2}$
View full solution →$a. \text{DDCE} \cong \text{DLDE};b. A B=B L;c. DC =\frac{ AL }{2}$
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