Class 9 Mathematics Triangles Congruence of Triangles

Easy

It is given that $\triangle ABC \cong \triangle RPQ$. Is it true to say that $BC = QR$? Why?

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Solution

(B) It is false to say that $BC = QR$.
Since $\triangle ABC \cong \triangle RPQ$,the corresponding parts of congruent triangles are equal $(CPCT)$.
By matching the vertices,we have $A \leftrightarrow R$,$B \leftrightarrow P$,and $C \leftrightarrow Q$.
Therefore,the side $BC$ corresponds to the side $PQ$.
Thus,$BC = PQ$,not $QR$.

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Class 9

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Chapter

Triangles

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Congruence of Triangles

Line $l$ is the bisector of an angle $\angle A$ and $B$ is any point on $l$. $BP$ and $BQ$ are perpendiculars from $B$ to the arms of $\angle A$ (see Fig). Show that :
$(i)$ $\Delta APB \cong \Delta AQB$
$(ii)$ $BP = BQ$ or $B$ is equidistant from the arms of $\angle A$.

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$ABC$ is a triangle in which altitudes $BE$ and $CF$ to sides $AC$ and $AB$ are equal (see Fig). Show that
$(i)$ $\Delta ABE \cong \Delta ACF$
$(ii)$ $AB = AC$,i.e.,$ABC$ is an isosceles triangle.

Medium

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In an isosceles triangle $ABC$,with $AB = AC$,the bisectors of $\angle B$ and $\angle C$ intersect each other at $O$. Join $A$ to $O$. Show that :
$(i)$ $OB = OC$
$(ii)$ $AO$ bisects $\angle A$

Medium

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In the figure,$AC = AE$,$AB = AD$ and $\angle BAD = \angle EAC$. Show that $BC = DE$.

Medium

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It is given that $\Delta PQR \cong \Delta EDF$. Is it true to say that $PR = EF$? Give a reason for your answer.

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It is given that $\triangle ABC \cong \triangle RPQ$. Is it true to say that $BC = QR$? Why?

Similar Questions

Line $l$ is the bisector of an angle $\angle A$ and $B$ is any point on $l$. $BP$ and $BQ$ are perpendiculars from $B$ to the arms of $\angle A$ (see Fig). Show that :$(i)$ $\Delta APB \cong \Delta AQB$$(ii)$ $BP = BQ$ or $B$ is equidistant from the arms of $\angle A$.

$ABC$ is a triangle in which altitudes $BE$ and $CF$ to sides $AC$ and $AB$ are equal (see Fig). Show that$(i)$ $\Delta ABE \cong \Delta ACF$$(ii)$ $AB = AC$,i.e.,$ABC$ is an isosceles triangle.

In an isosceles triangle $ABC$,with $AB = AC$,the bisectors of $\angle B$ and $\angle C$ intersect each other at $O$. Join $A$ to $O$. Show that :$(i)$ $OB = OC$$(ii)$ $AO$ bisects $\angle A$

In the figure,$AC = AE$,$AB = AD$ and $\angle BAD = \angle EAC$. Show that $BC = DE$.

It is given that $\Delta PQR \cong \Delta EDF$. Is it true to say that $PR = EF$? Give a reason for your answer.

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Line $l$ is the bisector of an angle $\angle A$ and $B$ is any point on $l$. $BP$ and $BQ$ are perpendiculars from $B$ to the arms of $\angle A$ (see Fig). Show that :
$(i)$ $\Delta APB \cong \Delta AQB$
$(ii)$ $BP = BQ$ or $B$ is equidistant from the arms of $\angle A$.

$ABC$ is a triangle in which altitudes $BE$ and $CF$ to sides $AC$ and $AB$ are equal (see Fig). Show that
$(i)$ $\Delta ABE \cong \Delta ACF$
$(ii)$ $AB = AC$,i.e.,$ABC$ is an isosceles triangle.

In an isosceles triangle $ABC$,with $AB = AC$,the bisectors of $\angle B$ and $\angle C$ intersect each other at $O$. Join $A$ to $O$. Show that :
$(i)$ $OB = OC$
$(ii)$ $AO$ bisects $\angle A$