Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Compute the value of x in the following figure:
Fill in the blank to make the following statement true:
A triangle cannot have more than ...... right angles.
An exterior angle of a triangle is equal to 100° and two interior opposite angles are equal. Each of these angles is equal to
One angle of a triangle is 61° and the other two angles are in the ratio `1 1/2: 1 1/3`. Find these angles.
In the following, find the marked unknown angle:
As shown in the figure, Avinash is standing near his house. He can choose from two roads to go to school. Which way is shorter? Explain why.
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.
12 cm, 12 cm, 16 cm
The angles of the triangle are 3x – 40, x + 20 and 2x – 10 then the value of x is
If an angle of a triangle is equal to the sum of the other two angles, find the type of the triangle
In the following figure, PQ ⊥ RQ, PQ = 5 cm and QR = 5 cm. Then ∆PQR is ______.
