Advertisements
Advertisements
प्रश्न
Find the values of x and y using the information shown in the figure.
Find the measure of ∠ABD and m∠ACD.
उत्तर
In ΔABC, AB = AC
∴ ∠ABC ≅ ∠ACB ...(Isosceles triangle theorem)
∴ ∠ACB = 50° ...(given)
∴ ∠ABC = 50° i.e. x = 50°
In ΔBDC, DB = DC
∴ ∠DBC = ∠DCB ...(Isosceles triangle theorem)
∠DBC = 60° ...(given)
∠DCB = 60° i.e. y = 60°
Now, ∠ABD = ∠ABC + ∠DBC ...(Angle addition property)
= 50° + 60°
= ∠ABD = 110°
Also, ∠ACD = ∠ACB + ∠DCB ...(Angle addition property)
= 50° + 60°
= 110°
∠ACD = 110°
Hence, the values of x = 50° and y = 60°, ∠ABD = 110° and ∠ACD = 110° respectively.
APPEARS IN
संबंधित प्रश्न
ΔABC is isosceles in which AB = AC. Seg BD and seg CE are medians. Show that BD = CE.
In triangle ABC, D is a point in AB such that AC = CD = DB. If ∠B = 28°, find the angle ACD.
ABC is an equilateral triangle. Its side BC is produced up to point E such that C is mid-point of BE. Calculate the measure of angles ACE and AEC.
In triangle ABC; angle ABC = 90o and P is a point on AC such that ∠PBC = ∠PCB.
Show that: PA = PB.
In triangle ABC; ∠A = 60o, ∠C = 40o, and the bisector of angle ABC meets side AC at point P. Show that BP = CP.
Using the information given of the following figure, find the values of a and b. [Given: CE = AC]
In triangle ABC, AB = AC; BE ⊥ AC and CF ⊥ AB.
Prove that:
(i) BE = CF
(ii) AF = AE
Through any point in the bisector of an angle, a straight line is drawn parallel to either arm of the angle. Prove that the triangle so formed is isosceles.
If the bisector of an angle of a triangle bisects the opposite side, prove that the triangle is isosceles.
