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2. (a) Explain what it means to say that two triangles are similar. (b) State a condition for two triangles to be similar that does not involve their angles. (A proof is not required). (c) Let ABC be a triangle, and suppose that ZCAB is a right angle. Drop a per- pendicular from A to BC with foot P. Show that ABC, PAC and PBA are all similar triangles.

2. (a) Explain what it means to say that two triangles are similar. (b) State a condition for two triangles to be similar that does not involve their angles. (A proof is not required). (c) Let ABC be a triangle, and suppose that ZCAB is a right angle. Drop a per- pendicular from A to BC with foot P. Show that ABC, PAC and PBA are all similar triangles.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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2. (a) Explain what it means to say that two triangles are similar. (b) State a condition for two triangles to be similar that does not involve their angles. (A proof is not required). (c) Let ABC be a triangle, and suppose that ZCAB is a right angle. Drop a per- pendicular from A to BC with foot P. Show that ABC, PAC and PBA are all similar triangles. (d) Using parts (b) and (c), or otherwise, show that in the triangle ABC from (c) that PC = 6² a and PB = 2 a where a = BC = the hypotenuse of ABC, b = AC and c = AB. Use this to give a proof of Pythagoras' Theorem.
Transcribed Image Text:2. (a) Explain what it means to say that two triangles are similar. (b) State a condition for two triangles to be similar that does not involve their angles. (A proof is not required). (c) Let ABC be a triangle, and suppose that ZCAB is a right angle. Drop a per- pendicular from A to BC with foot P. Show that ABC, PAC and PBA are all similar triangles. (d) Using parts (b) and (c), or otherwise, show that in the triangle ABC from (c) that PC = 6² a and PB = 2 a where a = BC = the hypotenuse of ABC, b = AC and c = AB. Use this to give a proof of Pythagoras' Theorem.
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