Advertisements
Advertisements
प्रश्न
Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.
Advertisements
उत्तर
It is given that
BC = AD
BC || AD
We have to prove that AB and CD bisect at O.
If we prove that ΔAOD ≅ ΔBOC , then
We can prove AB and CDbisects atO.
Now in ΔAOD and ΔBOC
AD = BC(Given)
∠OBC =∠OAD (Since AD || BC and AB is transversal)
And ∠OCB = ∠ODA(since AD || BC and CD is transversal)
So by ASAcongruence criterion we have,
ΔAOD ≅ ΔBOC, so
OA = OB
OD = OC
Hence ABand CD bisect each other at O.
APPEARS IN
संबंधित प्रश्न
ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that ∠BCD is a right angle.
AB is a line seg P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (See Fig. 10.26). Show that the line PQ is perpendicular bisector of AB.
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
Which of the following statements are true (T) and which are false (F):
Sides opposite to equal angles of a triangle may be unequal
Which of the following statements are true (T) and which are false (F) :
If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.
Which of the following statements are true (T) and which are false (F):
The two altitudes corresponding to two equal sides of a triangle need not be equal.
Fill the blank in the following so that the following statement is true.
If altitudes CE and BF of a triangle ABC are equal, then AB = ....
Which of the following statements are true (T) and which are false (F)?
Difference of any two sides of a triangle is equal to the third side.
Which of the following statements are true (T) and which are false (F)?
Of all the line segments that can be drawn from a point to a line not containing it, the perpendicular line segment is the shortest one.
If the angles of a triangle are in the ratio 2 : 1 : 3, then find the measure of smallest angle.
Line segments AB and CD intersect at O such that AC || DB. If ∠CAB = 45° and ∠CDB = 55°, then ∠BOD =
In the given figure, x + y =
In the given figure, if AB ⊥ BC. then x =
In the given figure, what is z in terms of x and y?
In the given figure, what is the value of x?
The side BC of ΔABC is produced to a point D. The bisector of ∠A meets side BC in L. If ∠ABC = 30° and ∠ACD = 115°, then ∠ALC = ______.
The angles of a right angled triangle are
In ∆ABC, BC = AB and ∠B = 80°. Then ∠A is equal to ______.
Is it possible to construct a triangle with lengths of its sides as 8 cm, 7 cm and 4 cm? Give reason for your answer.
