EXERCISE 4.8 #5 The diagonals of a trapezoid divide each other proportionally. Given: Trapezoid ABCD with diagonal AC, BD intersecting at 0 AO Prove: CO BO DO Statements Reasons 1. (see above) 2. AB || CD 1. Given 2. 3. If two parallel lines are cut by a transversal, then the alternate interior angles are =. 3. (Give 2 pairs of equal angles) 4. AAOB~ACOD 4. 5. 5. CO %D - DO B.
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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