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 and DBC are two isosceles triangles on the same base BC (see the given figure). Show that ∠ABD = ∠ACD.
In Fig. 10.23, PQRS is a square and SRT is an equilateral triangle. Prove that
(i) PT = QT (ii) ∠TQR = 15°
The vertical angle of an isosceles triangle is 100°. Find its base angles.
Prove that each angle of an equilateral triangle is 60°.
In ΔABC, if ∠A = 40° and ∠B = 60°. Determine the longest and shortest sides of the triangle.
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)
Which of the following statements are true (T) and which are false (F)?
Sum of any two sides of a triangle is greater than 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.
Fill in the blank to make the following statement true.
If two angles of a triangle are unequal, then the smaller angle has the........ side opposite to it.
Fill in the blank to make the following statement true.
If two sides of a triangle are unequal, then the larger side has .... angle opposite to it.
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.
ABC is a triangle. The bisector of the exterior angle at B and the bisector of ∠C intersect each other at D. Prove that ∠D = \[\frac{1}{2}\] ∠A.
Write the sum of the angles of an obtuse triangle.
In the given figure, if EC || AB, ∠ECD = 70° and ∠BDO = 20°, then ∠OBD is
If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle?
The angles of a right angled triangle are
Which of the following correctly describes the given triangle?
M is a point on side BC of a triangle ABC such that AM is the bisector of ∠BAC. Is it true to say that perimeter of the triangle is greater than 2 AM? Give reason for your answer.
Find all the angles of an equilateral triangle.
Show that in a quadrilateral ABCD, AB + BC + CD + DA > AC + BD
