Q11 of 76 Page 10

In Fig. 10.25, AB = AC and DB = DC, find the ratio ∠ABD:∠ACD.

Consider the figure,

Given,


AB = AC


DB = DC


To find: Ratio ∠ABD =∠ACD


Now, are isosceles triangles


Since, AB = AC


And,


DB = DC


Therefore, ∠ABC = ∠ACB and,


∠DBC = ∠DCB (Angle opposite equal sides)


Now, consider ∠ABD: ∠ACD


(∠ABC - ∠DBC): (∠ACB - ∠DCB)


(∠ABC - ∠DBC): (∠ABC - ∠DBC) [Since, ∠ABC = ∠ACB and ∠DBC = ∠DCB]


1: 1


Therefore, ∠ABD: ∠ACD = 1:1


More from this chapter

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9

Find the measure of each exterior angle of an equilateral triangle.

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If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.

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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.

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AB is a line segment. 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.