Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given in the question, P is a point on the bisector of ∠ABC. If the line through P, parallel to BA meet BC at Q.
To prove: BPQ is an isosceles triangle.
Proof: ∠1 = ∠2 ...(i) [BP is the bisector of ∠ABC]
PQ is parallel to BA and BP cuts them.
So, ∠1 = ∠3 ...[Alternate interior angles as PQ || AB]
∠2 = ∠3 ...[Proved above]
PQ = BQ ...[Sides opposite to equal angle are equal]
Hence, BPQ is an isosceles triangle.
APPEARS IN
संबंधित प्रश्न
If one angle of a triangle is equal to the sum of the other two, show that the triangle is a
right triangle.
Define a triangle.
Calculate the unknown marked angles of the following figure :
Find the value of the angle in the given figure:
In the given figure, show that: ∠a = ∠b + ∠c
(i) If ∠b = 60° and ∠c = 50° ; find ∠a.
(ii) If ∠a = 100° and ∠b = 55° : find ∠c.
(iii) If ∠a = 108° and ∠c = 48° ; find ∠b.
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.
17 cm, 7 cm, 8 cm
If an angle of a triangle is equal to the sum of the other two angles, find the type of the triangle
What is the sum of the measures of the interior angles of any triangle, △ABC?
The sides of a triangle must always be connected so that:
