State which pairs of triangles in the figure are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form.
(N/A) In $\triangle MNL$ and $\triangle QPR$:
Given $\angle M = \angle Q = 70^{\circ}$.
Also,the ratios of the sides including these angles are:
$\frac{MN}{QP} = \frac{2.5}{5} = \frac{1}{2}$
$\frac{ML}{QR} = \frac{5}{10} = \frac{1}{2}$
Since $\frac{MN}{QP} = \frac{ML}{QR} = \frac{1}{2}$ and $\angle M = \angle Q$,by the $SAS$ (Side-Angle-Side) similarity criterion,the two triangles are similar.
Therefore,$\triangle MNL \sim \triangle QPR$.
Given $\angle M = \angle Q = 70^{\circ}$.
Also,the ratios of the sides including these angles are:
$\frac{MN}{QP} = \frac{2.5}{5} = \frac{1}{2}$
$\frac{ML}{QR} = \frac{5}{10} = \frac{1}{2}$
Since $\frac{MN}{QP} = \frac{ML}{QR} = \frac{1}{2}$ and $\angle M = \angle Q$,by the $SAS$ (Side-Angle-Side) similarity criterion,the two triangles are similar.
Therefore,$\triangle MNL \sim \triangle QPR$.
Explore More
Similar Questions
In the figure,altitudes $AD$ and $CE$ of $\Delta ABC$ intersect each other at the point $P$. Show that $\Delta PDC \sim \Delta BEC$.
Easy
View Solution$D$ is a point on the side $BC$ of a triangle $ABC$ such that $\angle ADC = \angle BAC$. Show that $CA^2 = CB \cdot CD$.
Easy
View SolutionIn the figure,two chords $AB$ and $CD$ of a circle intersect each other at point $P$ (when produced) outside the circle. Prove that $\Delta PAC \sim \Delta PDB$.
Medium
View SolutionIn Figure,$CM$ and $RN$ are respectively the medians of $\Delta ABC$ and $\Delta PQR$. If $\Delta ABC \sim \Delta PQR$,prove that:
$(i)$ $\Delta AMC \sim \Delta PNR$
$(ii)$ $\frac{CM}{RN} = \frac{AB}{PQ}$
$(iii)$ $\Delta CMB \sim \Delta RNQ$
$(i)$ $\Delta AMC \sim \Delta PNR$
$(ii)$ $\frac{CM}{RN} = \frac{AB}{PQ}$
$(iii)$ $\Delta CMB \sim \Delta RNQ$
Difficult
View SolutionDiagonals of a trapezium $ABCD$ with $AB \parallel DC$ intersect each other at the point $O$. If $AB = 2 CD$,find the ratio of the areas of triangles $AOB$ and $COD$.
Difficult
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