Triangles — Class 10 Mathematics (Standard) PYQs

Devansh proved that $\Delta ABC\sim \Delta PQR$ using SAS similarity criteria. If he found $\angle C=\angle R$, then which of the following was proved true?

In the given figure, $PQ\parallel YZ$ such that $XP : PY = 2 : 3$. If $PQ=5\text{cm}$, then $YZ$ equals

In the given figure, $AB\parallel DE$ and $AC\parallel DF$. Show that $\Delta ABC\sim \Delta DEF$. If $BC=10\text{cm},EB=CF=5\text{cm}$ and $AB=7\text{cm}$, then find the length $DE$.

(a) D is the mid-point of side BC of $\Delta ABC$. CE and BF intersect at O, a point on AD. AD is produced to G such that $OD = DG$. Prove that
(i) OBGC is a parallelogram.
(ii) $EF\parallel BC$
(iii) $\Delta AEF\sim \Delta ABC$
OR
(b) Through the mid-point Q of side CD of a parallelogram ABCD, the line AR is drawn which intersects BD at P and produced BC at R. Prove that
(i) $AQ = QR$
(ii) $AP = 2PQ$
(iii) $PR = 2AP$

In the given figure, $AB\parallel EF$. If $AB=24\text{cm},EF=36\text{cm}$ and $DA=7\text{cm}$, then $AE$ equals

In triangles ABC and DEF, $\angle B=\angle E$, $\angle F=\angle C$ and $AB=3DE$. Then, the two triangles are :

(a) If $\Delta ABC\sim \Delta PQR$ in which $AB=6\text{cm},BC=4\text{cm},AC=8\text{cm}$ and $PR=6\text{cm}$, then find the length of $(PQ + QR)$.
OR
(b) In the given figure, $\frac{QR}{QS}=\frac{QT}{PR}$ and $\angle 1=\angle 2$, show that $\Delta PQS\sim \Delta TQR$.

(a) The diagonal BD of a parallelogram ABCD intersects the line segment AE at the point F, where E is any point on the side BC. Prove that $DF\times EF=FB\times FA$.
OR
(b) In $\Delta ABC$, if $AD\perp BC$ and $A{D}^2=BD\times DC$, then prove that $\angle BAC=90^{\circ }$.

In the given figure, $PQ\parallel BC$. If $\frac{AP}{PB}=\frac{4}{13}$ and $AC=20.4\text{cm}$, then the length of $AQ$ is :

Which of the following statements is incorrect ?