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. 4.8: Proving Lines Proportionál "Example - Given: AABC is an inscribed A; CE bisects LACB AD CD • Prove: EB CB п 2'. Reasons Statements 1. Given 1. (see above) 2. Def. of angle bisector. 2. 21 = 41' 3. Angles inscribed in the same segment or equal segments are equal. 3. 22 = L2' 4. a.a. 4. ΔΙ~ΔΙ AD 5. EB 5. CSSTP (corresponding sides of similar t are proportional) CD || CB
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. Also, THERE IS AN EXAMPLE OF HOW IT IS IN ONE OF THE PICTURES.
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.
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