In the adjoining figure, $ P Q=R S $ and $ Q R= $ SP. Find the third pair of corresponding parts that makes $ \Delta P Q R \cong \Delta $ PSR.
"
Given:
$PQ=RS$ and $QR=SP$
To do:
We have to find the third pair of corresponding parts that makes \( \Delta P Q R \cong \Delta \) PSR.
Solution:
In the above figure,
$PQ=RS$ (given)
$QR=SP$ (given)
$PR =PR$ (common side)
Therefore,
\( \Delta P Q R \cong \Delta \) PSR (By SSS congruency)
The third pair of corresponding parts that makes \( \Delta P Q R \cong \Delta \) PSR is $PR=PR$.
- Related Articles
- In the adjoining figure, $P R=S Q$ and $S R=P Q$.a) Prove that $\angle P=\angle S$.b) $\Delta SOQ \cong \Delta POR$."\n
- In the adjoining figure, $SP$ and $RQ$ are perpendiculars on the same line $PQ$. Prove that $\Delta P Q S \cong \Delta Q P R$."\n
- In the figure, \( O Q: P Q=3: 4 \) and perimeter of \( \Delta P O Q=60 \mathrm{~cm} \). Determine \( P Q, Q R \) and \( O P \)."\n
- In \( \Delta P Q R \), right-angled at \( Q, P Q=3 \mathrm{~cm} \) and \( P R=6 \mathrm{~cm} \). Determine \( \angle P \) and \( \angle R \).
- In the figure, common tangents \( P Q \) and \( R S \) to two circles intersect at \( A \). Prove that \( P Q=R S \)."\n
- In the figure, tangents \( P Q \) and \( P R \) are drawn from an external point \( P \) to a circle with centre $O$, such that \( \angle R P Q=30^{\circ} . \) A chord \( R S \) is drawn parallel to the tangent \( P Q \). Find \( \angle R Q S \)."\n
- If $p=-2,\ q=-1$ and $r=3$, find the value of $p-q-r$.
- If $p,\ q,\ r$ are in A.P., then show that $p^2( p+r),\ q^2( r+p),\ r^2( p+q)$ are also in A.P.
- In a triangle \( P Q R, N \) is a point on \( P R \) such that \( Q N \perp P R \). If \( P N \). \( N R=Q^{2} \), prove that \( \angle \mathrm{PQR}=90^{\circ} \).
- Simplify the following.a) \( (l^{2}-m^{2})(2 l+m)-m^{3} \)b) \( (p+q+r)(p-q+r)+p q-q r \)
- If p,q and r are in proportion and q =17, r=289, find p.
- Construct a triangle \( P Q R \) with side \( Q R=7 \mathrm{~cm}, P Q=6 \mathrm{~cm} \) and \( \angle P Q R=60^{\circ} \). Then construct another triangle whose sides are \( 3 / 5 \) of the corresponding sides of \( \triangle P Q R \).
- If $p=-2,\ q=-1$ and $r=3$, find the value of $p^{2}+q^{2}-r^{2}$.
- In the figure, \( P Q \) is tangent at a point \( R \) of the circle with centre \( O \). If \( \angle T R Q=30^{\circ} \), find \( m \angle P R S \)."\n
- In \( \Delta X Y Z, X Y=X Z \). A straight line cuts \( X Z \) at \( P, Y Z \) at \( Q \) and \( X Y \) produced at \( R \). If \( Y Q=Y R \) and \( Q P=Q Z \), find the angles of \( \Delta X Y Z \).
Kickstart Your Career
Get certified by completing the course
Get Started