In the given figure, Δ ABC is isosceles and AP x BQ = AC2, prove that Δ ACP ∼ Δ BCQ.

Given, ⇒ AP x BQ = AC2 ⇒ AP x BQ = AC x AC ⇒ AP x BQ = AC x BC (From figure, AC = BC) ⇒ ........................(1) Since, AC = BC ⇒ ∠CAB = ∠CBA ...............(2) [Angles opposite to equal sides are equal] ⇒ 180° - ∠CAB = 180° - ∠CBA ⇒ ∠CAP = ∠CBQ ...................(3) In Δ ACP and Δ BCQ, ⇒ ∠CAP = ∠CBQ [From equation (3)] ⇒ [From equation (1)] ∴ Δ ACP ∼ Δ BCQ (By SAS postulates) Hence, proved that Δ ACP ∼ Δ BCQ.

In triangle ABC, AD is perpendicular to side BC and AD² = BD × CD.
prove that angle BAC = 90°.

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In triangle ABC, ∠BAC = 90° and AD is perpendicular to side BC. Triangle ABD is similar to triangle CBA by :
SAS
ASA
AAA
RHS

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If AE = 10 cm, BD = 8 cm and BC = 10 cm, then AB is equal to :
5 cm
25 cm
12.5 cm
2.5 cm

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Mathematics

In the given figure, Δ ABC is isosceles and AP x BQ = AC², prove that Δ ACP ∼ Δ BCQ.

Similarity

Related Questions

In triangle ABC, AD is perpendicular to side BC and AD² = BD × CD.
prove that angle BAC = 90°.

In triangle ABC, ∠BAC = 90° and AD is perpendicular to side BC. Triangle ABD is similar to triangle CBA by :
SAS
ASA
AAA
RHS

If AE = 10 cm, BD = 8 cm and BC = 10 cm, then AB is equal to :
5 cm
25 cm
12.5 cm
2.5 cm

Mathematics

In the given figure, Δ ABC is isosceles and AP x BQ = AC2, prove that Δ ACP ∼ Δ BCQ.

Similarity

Related Questions

In triangle ABC, AD is perpendicular to side BC and AD2 = BD × CD.prove that angle BAC = 90°.

In triangle ABC, ∠BAC = 90° and AD is perpendicular to side BC. Triangle ABD is similar to triangle CBA by :SASASAAAARHS

If AE = 10 cm, BD = 8 cm and BC = 10 cm, then AB is equal to :5 cm25 cm12.5 cm2.5 cm

In the given figure, Δ ABC is isosceles and AP x BQ = AC², prove that Δ ACP ∼ Δ BCQ.

In triangle ABC, AD is perpendicular to side BC and AD² = BD × CD.
prove that angle BAC = 90°.

In triangle ABC, ∠BAC = 90° and AD is perpendicular to side BC. Triangle ABD is similar to triangle CBA by :
SAS
ASA
AAA
RHS

If AE = 10 cm, BD = 8 cm and BC = 10 cm, then AB is equal to :
5 cm
25 cm
12.5 cm
2.5 cm