In the figure, QR is parallel to AB and DR is parallel to QB. Prove that : PQ 2 = PD × PA.

In △PQR and △PAB, ∠PQR = ∠PAB [Corresponding angles are equal] ∠PRQ = ∠PBA [Corresponding angles are equal] Hence, △PQR ~ △PAB [By AA] Since, corresponding sides of similar triangles are proportional to each other. ........(1) In △PDR and △PQB, ∠PDR = ∠PQB [Corresponding angles are equal] ∠PRD = ∠PBQ [Corresponding angles are equal] Hence, △PDR ~ △PQB [By AA] Since, corresponding sides of similar triangles are proportional to each other. ........(2) From (1) and (2) we get : Hence, proved that PQ 2 = PD × PA.

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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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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Mathematics

In the figure, QR is parallel to AB and DR is parallel to QB.
Prove that : PQ² = PD × PA.

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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.

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.

Mathematics

In the figure, QR is parallel to AB and DR is parallel to QB.Prove that : PQ2 = PD × PA.

Similarity

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.

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 figure, QR is parallel to AB and DR is parallel to QB.
Prove that : PQ² = PD × PA.

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.

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.