4.7: Proving Triangles Similar Complete the following proofs and add the emphasized statements to your proven statements. Exercise 4.7 #1 Prove that two isosceles triangles are similar if any angle of one equals the corresponding angle of the other. A. B. b. Case 2: Equal Base Angles Given: Isosceles AABC, isosceles ADEF, AC = BC, DF = EF, %3D ZA = ZD Prove: AABC ADEF Statements Reasons 1. (see above) 1. Given 2. In any isosceles triangle, the angles opposite the equal sides are equal. 2. 3. Quantities that are equal to equal quantities are equal. 3. 4. AABC ~ ADEF 4.
About proofs. Please help finish the blanks. Maybe you will need 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. (I.I)
Theorem 59- If two triangles have their sides respectively proportional, then the triangles are similar. (s.s.s)
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