Advertisements
Advertisements
प्रश्न
Q is a point on the side SR of a ∆PSR such that PQ = PR. Prove that PS > PQ.
Advertisements
उत्तर
In triangle PSR, Q is a point on the side SR such that PQ = PR.
To proof that PS > PQ
Proof: In triangle PRQ,
PQ = PR ...[Given]
∠R = ∠PQR ...(i) [Angle opposite to equal sides are equal]
∠PQR > ∠S ...(ii) [Exterior angle of a triangle is greater than each of the opposite interior angle]
Now, from equation (i) and (ii), we get
∠R > ∠S
PS > PR ...[Side opposite to greater angle is longer]
PS > PQ ...[PQ = PR]
APPEARS IN
संबंधित प्रश्न
If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosce
In the given figure, AE bisects ∠CAD and ∠B= ∠C. Prove that AE || BC.
An exterior angle of a triangle is equal to 100° and two interior opposite angles are equal. Each of these angles is equal to
If the angles of a triangle are equal, find its angles.
In a triangle PQR, ∠P = 60° and ∠Q = ∠R, find ∠R.
In the following, find the marked unknown angle:
In the following figure, l || m and M is the mid-point of a line segment AB. Show that M is also the mid-point of any line segment CD, having its end points on l and m, respectively.
The image of an object placed at a point A before a plane mirror LM is seen at the point B by an observer at D as shown in the following figure. Prove that the image is as far behind the mirror as the object is in front of the mirror.
[Hint: CN is normal to the mirror. Also, angle of incidence = angle of reflection].
In the following figure, ∠BAC = 90° and AD ⊥ BC. The number of right triangles in the figure is ______.
In the following figure, PQ ⊥ RQ, PQ = 5 cm and QR = 5 cm. Then ∆PQR is ______.
