new.edmodo.com-Private 4.8: PROVING LINES PROPORTIONAL QOMPLETE THE FOLLOWING PROOFS. EXERCISE 4.8 #4 AD AC %3D CD PC * ABC is an inscribed triangle and chord AD bisects angle A and cuts BC at P. Prove: Given: Inscribed AABC, chord AD bisects ZA & cuts BC at P; chord CD AD AC Prove: CD %3D PC ' Reasons Statements 1. Given 1. (see above) 2. 2. ZD = ZD 3. Definition of angle bisectors 3. A. 4. ZBCD = ZDAB 5. Substitution 5. 6. 6. ДАСD~ДСPD AD 7. CD AC 7. %3D PC
About proofs. Please help finish the blanks. *Maybe you will have to use some of these theorems to prove the statement true...according to this unit.
Theorem 57- If two
Corollary 57-1 If two angles of one triangle are equal respectively to two angles of another, then the triangles are similar. (a.a.)
Corollary 57-2 Two right triangles are similar if an acute angle of one is equal to an acute angle of the other.
Theorem 58-If two triangles have two pairs of sides proportional and the included angles equal respectively, then the two triangles are similar. (s.a.s.)
Corollary 58-1 If the legs of one right triangle are proportional to the legs of another, the triangles are similar. (l.l.)
Theorem 59- If two triangles have their sides respectively proportional, then the triangles are similar. (s.s.s.)
Theorem 60- If two parallels are cut by three or more transversals passing through a common point, then the corresponding segments of the parallels are proportional.
C.A.S.T.E. - corresponding angles of similar triangles are equal
C.S.S.T.P. - corresponding sides of similar triangles are proportional
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