Given : ABCD is a rhombus, DPR and CBR are straight lines. Prove that : DP × CR = DC × PR.

Since, ABCD is a rhombus. So, AD || BC. In △DPA and △RPC, ⇒ ∠DPA = ∠RPC (Vertically opposite angles are equal) ⇒ ∠PAD = ∠PCR [Since, AD || CD and AC is transversal] ∴ △DPA ~ △RPC [By AA] Since, corresponding sides of similar triangles are proportional we have : ⇒ ..........(1) In rhombus all sides are equal. ∴ AD = DC Substituting in (1) we get, ⇒ ⇒ DP × CR = DC × PR. Hence, proved that DP × CR = DC × PR.

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

Given : ABCD is a rhombus, DPR and CBR are straight lines.
Prove that :
DP × CR = DC × PR.

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.

Mathematics

Given : ABCD is a rhombus, DPR and CBR are straight lines.Prove that :DP × CR = DC × PR.

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.

Given : ABCD is a rhombus, DPR and CBR are straight lines.
Prove that :
DP × CR = DC × PR.

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.