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Mathematics, 02.09.2021 03:30 ganggang6223

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If AB¯¯¯¯¯¯¯¯≅CB¯¯¯¯¯¯¯¯ is given, how can it be proved that m∠A=m∠C?

A. Draw a segment from B to a point D such that D is the midpoint of AC¯¯¯¯¯¯¯¯. Show that corresponding sides and the angle between these sides of new triangles ABD and CBD are congruent. Finally, use the Side-Angle-Side Congruence Postulate and the definition of congruent angles to show m∠A=m∠C

B. Draw a segment from B to a point D such that D is the midpoint of AC¯¯¯¯¯¯¯¯. Then, use the Triangle Sum Theorem to show m∠A=m∠C.

C. Draw a segment from B to a point D such that D is the midpoint of AC¯¯¯¯¯¯¯¯. Then, use the definition of isosceles triangles to show m∠A=m∠C.

D. Draw a segment from B to a point D such that D is the midpoint of AC¯¯¯¯¯¯¯¯. Then, show that corresponding sides of new triangles ABD and CBD are congruent. Finally, use the Side-Side-Side Congruence Postulate and the definition of congruent angles to show m∠A=m∠C.


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