In the given figure, AB = BC and AC = CD. Show that: ∠BAD : ∠ADB = 3 : 1

In △ABC, AB = BC ⇒ ∠BAC = ∠ACB = x (let) (Angles opposite to equal sides in a triangle are equal) In △ACD, AC = CD ⇒ ∠CAD = ∠ADC = y (let) (Angles opposite to equal sides in a triangle are equal) From figure, ⇒ ∠ACB + ∠ACD = 180° (Linear pair) ⇒ x + ∠ACD = 180° ⇒ ∠ACD = 180° - x In △ACD, By angle sum property of triangle, ⇒ ∠CAD + ∠ADC + ∠ACD = 180° ⇒ y + y + (180° - x) = 180° ⇒ 2y + 180° - x = 180° ⇒ 2y - x = 0 ⇒ 2y = x From figure, ∠BAD = ∠BAC + ∠CAD ⇒ ∠BAD = x + y ⇒ ∠BAD = 2y + y ⇒ ∠BAD = 3y ⇒ ∠BAD = 3∠ADC From figure, ⇒ ∠ADC = ∠ADB Thus, ⇒ ∠BAD = 3∠ADB ⇒ Hence, proved that ∠BAD : ∠ADB = 3 : 1.

In the given figure, AB = AD; CB = CD; ∠A = 42° and ∠C = 108°, find ∠ABC.

View Answer Bookmark Now

In the given figure, side BA of △ABC has been produced to D such that CD = CA and side CB has been produced to E. If ∠BAC = 106° and ∠ABE = 128°, find ∠BCD.

View Answer Bookmark Now

Show that the perpendiculars drawn from the extremities of the base of an isosceles triangle to the opposite sides are equal.

View Answer Bookmark Now

In a △ABC, AB = AC. If the bisectors of ∠B and ∠C meet AC and AB at points D and E respectively, show that :
(i) △DBC ≅ △ECB
(ii) BD = CE

View Answer Bookmark Now

Mathematics

In the given figure, AB = BC and AC = CD. Show that: ∠BAD : ∠ADB = 3 : 1

Triangles

Related Questions

In the given figure, AB = AD; CB = CD; ∠A = 42° and ∠C = 108°, find ∠ABC.

In the given figure, side BA of △ABC has been produced to D such that CD = CA and side CB has been produced to E. If ∠BAC = 106° and ∠ABE = 128°, find ∠BCD.

Show that the perpendiculars drawn from the extremities of the base of an isosceles triangle to the opposite sides are equal.

In a △ABC, AB = AC. If the bisectors of ∠B and ∠C meet AC and AB at points D and E respectively, show that :
(i) △DBC ≅ △ECB
(ii) BD = CE

Mathematics

In the given figure, AB = BC and AC = CD. Show that: ∠BAD : ∠ADB = 3 : 1

Triangles

Related Questions

In the given figure, AB = AD; CB = CD; ∠A = 42° and ∠C = 108°, find ∠ABC.

In the given figure, side BA of △ABC has been produced to D such that CD = CA and side CB has been produced to E. If ∠BAC = 106° and ∠ABE = 128°, find ∠BCD.

Show that the perpendiculars drawn from the extremities of the base of an isosceles triangle to the opposite sides are equal.

In a △ABC, AB = AC. If the bisectors of ∠B and ∠C meet AC and AB at points D and E respectively, show that :(i) △DBC ≅ △ECB(ii) BD = CE

In a △ABC, AB = AC. If the bisectors of ∠B and ∠C meet AC and AB at points D and E respectively, show that :
(i) △DBC ≅ △ECB
(ii) BD = CE