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
In the given figure, AB || DE. Find ∠ACD.
Fill in the blank to make the following statement true:
A triangle cannot have more than ...... right angles.
In ΔABC, if bisectors of ∠ABC and ∠ACB intersect at O at angle of 120°, then find the measure of ∠A.
In the given figure, side BC of ΔABC is produced to point D such that bisectors of ∠ABC and ∠ACD meet at a point E. If ∠BAC = 68°, find ∠BEC.
If the sides of a triangle are produced in order, then the sum of the three exterior angles so formed is
State, if the triangle is possible with the following angles :
125°, 40°, and 15°
The angle of a vertex of an isosceles triangle is 100°. Find its base angles.
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.
What is common in the following figure?
 |
 |
| (i) | (ii) |
Is figure (i) that of triangle? if not, why?
