In triangles $ABC$ and $PQR$,$\angle A = \angle Q$ and $\angle B = \angle R$. Which side of $\triangle PQR$ should be equal to side $BC$ of $\triangle ABC$ so that the two triangles are congruent? Give reason for your answer.
(N/A) In triangles $ABC$ and $PQR$,we are given:
$\angle A = \angle Q$ and $\angle B = \angle R$.
For the two triangles to be congruent by the $AAS$ (Angle-Angle-Side) congruence rule,the side corresponding to $BC$ in $\triangle ABC$ must be equal to the side corresponding to $RP$ in $\triangle PQR$.
Therefore,$BC = RP$.
This ensures that the two triangles are congruent by the $AAS$ congruence criterion.
$\angle A = \angle Q$ and $\angle B = \angle R$.
For the two triangles to be congruent by the $AAS$ (Angle-Angle-Side) congruence rule,the side corresponding to $BC$ in $\triangle ABC$ must be equal to the side corresponding to $RP$ in $\triangle PQR$.
Therefore,$BC = RP$.
This ensures that the two triangles are congruent by the $AAS$ congruence criterion.
Explore More
Similar Questions
State whether each of the following statements is true or false:
$(1)$ In $\Delta XYZ$,if $XY > XZ$,then $\angle Z > \angle Y$.
$(2)$ In $\Delta ABC$ and $\Delta PQR$,if $\frac{AB}{PR} = \frac{BC}{QP} = \frac{CA}{RQ} = 1$,then $\Delta ABC \cong \Delta RPQ$.
$(1)$ In $\Delta XYZ$,if $XY > XZ$,then $\angle Z > \angle Y$.
$(2)$ In $\Delta ABC$ and $\Delta PQR$,if $\frac{AB}{PR} = \frac{BC}{QP} = \frac{CA}{RQ} = 1$,then $\Delta ABC \cong \Delta RPQ$.
Medium
View Solution$ABC$ is an isosceles triangle with $AB = AC$. $BD$ and $CE$ are its two medians. Show that $BD = CE$.
Medium
View SolutionIn the given figure,$AB = AC$ and $BP = CQ$. Prove that $\Delta APQ$ is an isosceles triangle.
Medium
View SolutionIn $\Delta ABC$ and $\Delta PQR$,if $\angle B = \angle P = 90^{\circ}$,$AC = RQ$,and $AB = RP$,then $\Delta ABC \cong \Delta \ldots \ldots \ldots$
Easy
View SolutionIn quadrilateral $PQRS$,$PQ = PS$ and $QR = RS$. Prove that diagonal $PR$ bisects $\angle QPS$ as well as $\angle QRS$.
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo