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.
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 :
All the angles of a triangle can be less than 60°
Is the following statement true and false :
All the angles of a triangle can be equal to 60°.
In the given figure, AE bisects ∠CAD and ∠B= ∠C. Prove that AE || BC.
If the side BC of ΔABC is produced on both sides, then write the difference between the sum of the exterior angles so formed and ∠A.
Find the value of the angle in the given figure:
Find x, if the angles of a triangle is:
x°, 2x°, 2x°
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
In the following figure, points lying in the interior of the triangle PQR are ______, that in the exterior are ______ and that on the triangle itself are ______.
