ABC is a right angled triangle with ∠ABC = 90°. D is any point on AB and DE is perpendicular to AC. Prove that : (i) △ADE ~ △ACB (ii) If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD. (iii) Find, area of △ADE : area of quadrilateral BCED.

(i) In △ADE and △ACB, ⇒ ∠AED = ∠ABC [Both = 90°] ⇒ ∠EAD = ∠CAB [Common angle] ∴ △ADE ~ △ACB [By AA]. Hence, proved that △ADE ~ △ACB. (ii) In right angle triangle ABC, ⇒ AC 2 = AB 2 + BC 2 ⇒ 13 2 = AB 2 + 5 2 ⇒ 169 = AB 2 + 25 ⇒ AB 2 = 144 ⇒ AB = = 12 cm. Since, △ADE ~ △ACB and corresponding sides of similar triangles are proportional to each other. Hence, DE = cm. (iii) From figure, Area of △ADE = Area of quadrilateral BCED = Area of △ABC - Area of △ADE Hence, area of △ADE : area of quadrilateral BCED = 1 : 8.

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In the given figure, ABC is a right angled triangle with ∠BAC = 90°.
(i) Prove that : △ADB ~ △CDA.
(ii) If BD = 18 cm and CD = 8 cm, find AD.
(iii) Find the ratio of the area of △ADB is to area of △CDA.

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In the given figure, ABC is a triangle with ∠EDB = ∠ACB. Prove that △ABC ~ △EBD. If BE = 6 cm, EC = 4 cm, BD = 5 cm and area of △BED = 9 cm². Calculate the :
(i) length of AB
(ii) area of △ABC

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Mathematics

ABC is a right angled triangle with ∠ABC = 90°. D is any point on AB and DE is perpendicular to AC. Prove that :
(i) △ADE ~ △ACB
(ii) If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD.
(iii) Find, area of △ADE : area of quadrilateral BCED.

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Related Questions

In the given figure, ABC is a right angled triangle with ∠BAC = 90°.
(i) Prove that : △ADB ~ △CDA.
(ii) If BD = 18 cm and CD = 8 cm, find AD.
(iii) Find the ratio of the area of △ADB is to area of △CDA.

In the given figure, ABC is a triangle with ∠EDB = ∠ACB. Prove that △ABC ~ △EBD. If BE = 6 cm, EC = 4 cm, BD = 5 cm and area of △BED = 9 cm². Calculate the :
(i) length of AB
(ii) area of △ABC

Mathematics

ABC is a right angled triangle with ∠ABC = 90°. D is any point on AB and DE is perpendicular to AC. Prove that :(i) △ADE ~ △ACB(ii) If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD.(iii) Find, area of △ADE : area of quadrilateral BCED.

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Related Questions

In the given figure, ABC is a right angled triangle with ∠BAC = 90°.(i) Prove that : △ADB ~ △CDA.(ii) If BD = 18 cm and CD = 8 cm, find AD.(iii) Find the ratio of the area of △ADB is to area of △CDA.

In the given figure, ABC is a triangle with ∠EDB = ∠ACB. Prove that △ABC ~ △EBD. If BE = 6 cm, EC = 4 cm, BD = 5 cm and area of △BED = 9 cm2. Calculate the :(i) length of AB(ii) area of △ABC

ABC is a right angled triangle with ∠ABC = 90°. D is any point on AB and DE is perpendicular to AC. Prove that :
(i) △ADE ~ △ACB
(ii) If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD.
(iii) Find, area of △ADE : area of quadrilateral BCED.

In the given figure, ABC is a right angled triangle with ∠BAC = 90°.
(i) Prove that : △ADB ~ △CDA.
(ii) If BD = 18 cm and CD = 8 cm, find AD.
(iii) Find the ratio of the area of △ADB is to area of △CDA.

In the given figure, ABC is a triangle with ∠EDB = ∠ACB. Prove that △ABC ~ △EBD. If BE = 6 cm, EC = 4 cm, BD = 5 cm and area of △BED = 9 cm². Calculate the :
(i) length of AB
(ii) area of △ABC