Task 1

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Congruent Triangles

In this activity, you will use the GeoGebra geometry tool to explore the relationships among the sides and angles ofcongruent triangles.If you need help, follow theseinstructionsfor using GeoGebra.

Part A

Question

Perform the following series of rigid transformations on ABC:

• Translate ABCby moving it 5 units to the right and 2 units up.
• Draw the liney= -x, and reflect A'B'C'across the line.
• Rotate A''B''C''counterclockwise about the origin by 270.
• Lines
• Shapes
• Fill:
• Line:
• Width:1 pt
• 2 pt
• 3 pt
• 4 pt
• 5 pt
• 6 pt
• 7 pt
• 8 pt
• 9 pt
• 10 pt
• 16 pt
• 22 pt

Part B

Measure the angles of ABCand its three images, and record the measurements in the table.Round each answer to the nearest degree.

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Part C

Measure the lengths of the sides of ABCand its three images, and record the measurements in the table.

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Part D

How do the measures of the sides and angles of ABCcompare with the corresponding measurements in the three images?

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Part E

Translations, rotations, and reflections are rigid transformations.What can you conclude about the measures of sides and angles on any triangle after undergoing a series of rigid transformations?Explain.

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Part F

By definition, two shapes are congruent if you can map one onto the other using rigid transformations (a sequence of one or more rotations, translations, and reflections).Since any sequence of rigid transformations performed on a triangle results in a congruent triangle, what does that imply about the corresponding side lengths and angle measures for two congruent triangles?

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Characters used:92 / 15000

Part G

If two triangles have three corresponding angles and three corresponding sides that are equal in measure, are the two triangles necessarily congruent?Why?

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Characters used:119 / 15000