Advertisements
Advertisements
प्रश्न
In figure, AB = AC and DB = DC, find the ratio ∠ABD : ∠ACD
Advertisements
उत्तर
Consider the figure Given
AB = AC, DB = DC and given to find the ratio
∠ABD = ∠ACD
Now,∠ABC and ∠DBC are isosceles triangles since AB = AC and
DB = DC respectively
⇒ ∠ABC = ∠ACB and ∠DBC = ∠DCB [ ∵ angles opposite to equal sides are equal]
Now consider,
∠ABD : ∠ACD
⇒ (∠ABC - ∠DBC ) : (∠ACB - ∠DCB)
⇒ (∠ABC - ∠DBC ) : (∠ABC - ∠DBC ) [∵∠ABC - ∠ACB and ∠DBC = ∠DCB]
⇒ 1:1
∴∠ABD :∠ACD = 1:1
APPEARS IN
संबंधित प्रश्न
ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see the given figure). Show that these altitudes are equal.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
In Fig. 10.40, it is given that RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT
Find the measure of each exterior angle of an equilateral triangle.
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.
Angles A, B, C of a triangle ABC are equal to each other. Prove that ΔABC is equilateral.
In a ΔPQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP
respectively. Prove that LN = MN.
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.
Sides opposite to equal angles of a triangle are ......
Fill the blank in the following so that the following statement is true.
In an isosceles triangle ABC with AB = AC, if BD and CE are its altitudes, then BD is …… CE.
In a ΔABC, if ∠B = ∠C = 45°, which is the longest side?
O is any point in the interior of ΔABC. Prove that
(i) AB + AC > OB + OC
(ii) AB + BC + CA > OA + QB + OC
(iii) OA + OB + OC >` 1/2`(AB + BC + CA)
Prove that the perimeter of a triangle is greater than the sum of its altitudes.
In the given figure, the sides BC, CA and AB of a Δ ABC have been produced to D, E and F respectively. If ∠ACD = 105° and ∠EAF = 45°, find all the angles of the Δ ABC.
In the given figure, if BP || CQ and AC = BC, then the measure of x is
The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =
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 = ______.
In ∆ABC, AB = AC and ∠B = 50°. Then ∠C is equal to ______.
If ∆PQR ≅ ∆EDF, then is it true to say that PR = EF? Give reason for your answer
