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orlando19882000
orlando19882000
22.08.2019 • 
Mathematics

Given: abcd is a parallelogram. prove: ∠a≅∠c and ∠b≅∠d the quadrilateral abcd is a parallelogram, so, by definition, ab∥cd and ad∥bc. postulate 01-01 allows the construction of ac, which is a transversal of both sets of parallel lines. the theorem then supports the conclusion that ∠≅∠ and ∠3≅∠4. by the reflexive property of congruence, ac≅ac. therefore, △abc≅△cda by the asa congruence theorem. since corresponding parts of congruent triangles are congruent, we may conclude that ∠b≅∠d. to prove ∠a≅∠c, follow a similar argument beginning with construction bd. enter your answers as the word/phrase that fills in the first blank in statement 3 along with the numbers that fill in the second and third blanks in the statement. separate your answers with commas, like this: corresponding angles, 42, 53

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