Prove the triangles are similar. Write the Statements and Reasons.
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Prove the triangles are similar.Statements: 1) Angle A is congruent to Angle D (Given)2) Angle B is congruent to Angle E (Given)3) Angle C is congruent to Angle F (Given)Reasons:1) Definition of congruent angles2) Definition of congruent angles3) Definition of congruent angles
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To prove that two triangles are similar, you can follow these general steps, using the Angle-Angle (AA) criterion for similarity:
Statements and Reasons:
1) Statement: Angle A = Angle D
Reason: Given (or by corresponding angles if the triangles are positioned with parallel lines).
2) Statement: Angle B = Angle E
Reason: Given (or by corresponding angles).
3) Statement: Triangle ABC ~ Triangle DEF
Reason: By AA criterion, if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.
### Explanation:
Triangles are similar if they have the same shape but not necessarily the same size. This means that their corresponding angles are equal, which is proved using the angles provided in the statements. Once you establish that two angles in each triangle are equal, you can conclude that the triangles are similar.
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