Look at the triangles in the diagram.
Which of the following statements is true?
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Look at the triangles in the diagram.
Which of the following statements is true?
According to the existing data:
(Side)
(Side)
The angles equal to 53 degrees are both opposite the greater side (which is equal to 13) in both triangles.
(Angle)
Since the sides and angles are equal among congruent triangles, it can be determined that angle DEF is equal to angle BAC
Angles BAC is equal to angle DEF.
Look at the triangles in the diagram.
Which of the statements is true?
Look at the sides that form each angle. In triangle ABC, angle BAC is between sides BA and AC. In triangle DEF, angle DEF is between sides DE and EF. Since BA=EF=10 and AC=DE=13, these angles correspond.
The 53° angles are opposite the longest sides in both triangles. Since ED=AC=13 (the longest sides), and both triangles have a 53° angle opposite these sides, this helps confirm the triangles have the same shape.
Congruent triangles have exactly the same size and shape. All corresponding sides are equal and all corresponding angles are equal. They're like identical copies that might just be rotated or flipped.
If you have all three sides equal (SSS), yes! But in this problem, we're also given angle measurements, so we can use Side-Angle-Side (SAS) reasoning to identify corresponding parts.
Match vertices that are in similar positions. Since BA=EF=10, AC=ED=13, and both have 53° angles in corresponding positions, vertex A corresponds to vertex E, B to F, and C to D.
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