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
Mark the correct alternative in each of the following:
If all the three angles of a triangle are equal, then each one of them is equal to
Calculate the unknown marked angles of the following figure :
In the following, find the marked unknown angle:
In ∆ABC, C = 56° C = 56° ∠B = ∠C and ∠A = 100° ; find ∠B.
Classify the following triangle according to angle:
The length of the three segments is given for constructing a triangle. Say whether a triangle with these sides can be drawn. Give the reason for your answer.
17 cm, 7 cm, 8 cm
Bisectors of the angles B and C of an isosceles triangle with AB = AC intersect each other at O. BO is produced to a point M. Prove that ∠MOC = ∠ABC.
P is a point on the bisector of ∠ABC. If the line through P, parallel to BA meet BC at Q, prove that BPQ is an isosceles triangle.
Identify three triangles in the figure.
How is a vertex of triangle △ABC most accurately defined?
