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9-12 Integrated Math 1 Unit 2 Lesson 4

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K-5 Math 6-8 Math •9-12 Math

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•Integrated Math 1 Integrated Math 2 Integrated Math 3

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Unit 1 •Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9

Modeling Prompts

Lesson

Lesson 1 Lesson 2 Lesson 3 •Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11

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6-8
9-12

Integrated Math 1
Integrated Math 2
Integrated Math 3

Algebra 1
Geometry
Algebra 2
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Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9

Modeling Prompts

Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11

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Unit 2, Lesson 4

Congruent Triangles, Part 2

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Integrated Math 1

Practice

Problem 1
Student Task Statement
Match each statement using only the information shown in the pairs of congruent triangles.

In the two triangles there are 3 pairs of congruent sides.

The 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle.

The 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle.

Two adjacent triangles, sharing no sides, with the same orientation. The bottom side of both triangles is unmarked. The left side of each triangle has one tick mark, the upward facing angles each have one tick mark, and the right side of the triangles each have 2 tick marks.
Two adjacent congruent angles. One side of each triangle overlaps. The angles facing upwards next to the overlapping side in each triangle have 1 tick mark, the angles facing down next to the overlapping side each have two tick marks. The third angle is unmarked.

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Problem 2

Student Task Statement

Sketch the unique triangles that can be made with angle measures and and side length 3. How many unique triangles are there? How do you know you have sketched all possibilities?

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Problem 3

Student Task Statement

What is the least amount of information that you need to construct a triangle congruent to this one?

<p>Triangle JKL.</p>

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Problem 4

ForLesson 3: Congruent Triangles, Part 1

Student Task Statement

Triangle is congruent to triangle . So Mai knows that there is a sequence of rigid motions that takes to .

<p>Congruent triangles ABC and EFG.</p>

Select all true statements after the transformations:

Angle coincides with angle .

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Problem 5

ForLesson 3: Congruent Triangles, Part 1

Student Task Statement

A rotation by angle using point as the center takes triangle onto triangle .

<p>Triangle CBA and CDE.</p>

Explain why the image of segment lines up with segment .
Explain why the image of coincides with .
Is triangle congruent to triangle ? Explain your reasoning.

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Problem 6

ForLesson 2: Congruent Parts, Part 2

Student Task Statement

Line is a line of symmetry for figure . Clare says that is congruent to because sides and are corresponding.

<p>Line EF is a line of symmetry for figure ABECDF.</p>

Why is Clare's congruence statement incorrect?
Write a correct congruence statement for the quadrilaterals.

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Problem 7

ForLesson 2: Congruent Parts, Part 2

Student Task Statement

Triangle is the image of triangle after a reflection across line . Select all statements that must be true.

<p>Triangle H E F is the image of triangle H G F.</p>

Triangle is congruent to triangle .

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Problem 8

ForLesson 1: Congruent Parts, Part 1

Student Task Statement

When rectangle is reflected across line , the image is . How do you know that segment is congruent to segment ?

<p>Rectangle ABCD with line EF through lines AB and DC at midpoints E and F.</p>

A rectangle has 2 pairs of parallel sides.
Any 2 sides of a rectangle are congruent.
Corresponding parts of congruent figures are congruent.
Congruent parts of congruent figures are corresponding.

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Problem 9

ForLesson 19: Now What Can You Build?

Student Task Statement

This design began from the construction of a regular hexagon. Describe a rigid motion that will take the figure onto itself.

<p>Hexagon with line segments.</p>

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Lesson 4 Resources

Student Materials Student Materials in Spanish

Angle coincides with angle .

Segment coincides with segment .

Segment coincides with segment .

Segment coincides with segment .

Triangle is congruent to triangle .

Angle is congruent to angle .

Angle is congruent to angle .

Segment is congruent to segment .

Segment is congruent to segment .