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9-12 Geometry Unit 2 Lesson 2

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K-5 Math 6-8 Math •9-12 Math

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Algebra 1 •Geometry Algebra 2 Extra Support Materials for Algebra 1

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Unit 1 •Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8

Modeling Prompts

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Lesson 1 •Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15

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9-12

Algebra 1
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Algebra 2
Extra Support Materials for Algebra 1

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Unit 4
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Unit 8

Modeling Prompts

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Lesson 2

2.1 Warm-up 2.2 Activity 2.3 Activity Student Lesson Summary

Unit 2, Lesson 2

Congruent Parts, Part 2

Geometry

2.1

Warm-up

Math Talk: Which Are Congruent?

Each pair of figures is congruent. Decide whether each congruence statement is true or false.

<p>Triangles A B C and D E F.</p>

Triangle is congruent to triangle .

<p>Concave quadrilaterals Z P M J and Y B L X.</p>

Quadrilateral is congruent to quadrilateral .

<p>Triangles J K L and Q R S. Angles J L K and Q R S appear to be right angles.</p>

Triangle is congruent to triangle .

<p>Pentagons A B C D E and P Q R S T.</p>

Pentagon is congruent to pentagon .

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2.2

Activity

Which Triangles Are Congruent?

Here are 3 triangles.

<p>Triangles A C E, P Q R, and L M N. They each have 1 angle of 46 point 6 degrees. They each have 2 sides of lengths 4 point 3 and 5 point 9.</p>

Triangle is congruent to which triangle? Explain your reasoning.
Show a sequence of rigid motions that takes triangle to that triangle. Draw each step of the transformation.
Explain why there can’t be a rigid motion from triangle to the other triangle.

2.3

Activity

Are These Parts Congruent?

<p>Triangles A B D and C D B. Point E located on side D B.</p>

<p>Two concave polygons, G F O N M and H I J K L. G, H, M, and L are collinear.</p>

Triangle is a rotation of triangle around point by . Is angle congruent to angle ? If so, explain your reasoning. If not, which angle is congruent to?
Polygon is a reflection and translation of polygon . Is segment congruent to segment ? If so, explain your reasoning. If not, which segment is congruent to?
Quadrilateral is a rotation of polygon . Is angle congruent to angle ? If so, explain your reasoning. If not, which angle is congruent to?

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Student Lesson Summary

Naming congruent figures so it’s clear from the name which parts correspond makes it easier to check whether two figures are congruent and to use corresponding parts. In this image, segment appears to be congruent to segment . Also, segment appears to be congruent to segment . So, it makes more sense to conjecture that triangle is congruent to triangle than to conjecture triangle is congruent to triangle .

<p>Triangles E F D and A B C.</p>

If we are told quadrilateral is congruent to quadrilateral , without even looking at the figures we know:

Angle is congruent to angle .
Angle is congruent to angle .
Angle is congruent to angle .
Angle is congruent to angle .

Segments and are congruent.
Segments and are congruent.
Segments and are congruent.
Segments and are congruent.

Quadrilaterals and can be named in many different ways so that they still correspond—such as is congruent to , or is congruent to . But is congruent to means there are different corresponding parts. Note that quadrilateral refers to a different way of connecting the points than quadrilateral .

<p>3 quadrilaterals: M A T H, L O V E, and A T M H. In quadrilateral A T M H, sides T M and H A cross over each other.</p>

Glossary

None

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