Advertisements
Advertisements
Question
Q is a point on the side SR of a ∆PSR such that PQ = PR. Prove that PS > PQ.
Advertisements
Solution
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
RELATED QUESTIONS
If one angle of a triangle is equal to the sum of the other two, show that the triangle is a
right triangle.
ABC is a triangle in which ∠A — 72°, the internal bisectors of angles B and C meet in O.
Find the magnitude of ∠BOC.
Determine the measure of each of the equal angles of a right-angled isosceles triangle.
OR
ABC is a right-angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
Is the following statement true and false :
An exterior angle of a triangle is greater than the opposite interior angles.
Calculate the unknown marked angles of the following figure :
One of the base angles of an isosceles triangle is 52°. Find its angle of the vertex.
One angle of a right-angled triangle is 70°. Find the other acute angle.
Classify the following triangle according to sides:
Classify the following triangle according to sides:
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.
7 cm, 24 cm, 25 cm
