EXERCISE 4.8 #10 The product of any side of a triangle and its altitude (height) is equal to the product of any other side and its altitude. Given: AABC, altitudes AE & CD Prove: AB · CD = CB · AE B. Statements Reasons 1. (see above) 1. Given 2. In a triangle, the two triangles formed by 2 sides and the altitudes on those sides are similar. 2. AAEB~ACDB (Exercises 4.7 #4) 3. AB 3. CB AE %3D CD 4. AB · CD = CB · AE 4.
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.
If a line is drawn parallel to the base of a triangle, it cuts off a triangle similar to the given triangle.
Two isosceles
Theorem 57- If two triangles have the three angles of one equal respectively to the three angles of the other, then the triangles are similar
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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