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9-12 Geometry Unit 2 Lesson 11

Gradeband

K-5 Math 6-8 Math •9-12 Math

Course

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

Unit

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

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 Lesson 12 Lesson 13 Lesson 14 Lesson 15

K-5
6-8
9-12

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Integrated Math 1
Integrated Math 2
Integrated Math 3

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

Modeling Prompts

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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Unit 2, Lesson 11

Side-Side-Angle (Sometimes) Congruence (Optional)

Geometry

Practice

Problem 1
Student Task Statement
Which of the following criteria always proves triangles congruent? Select all that apply.

3 congruent angles

3 congruent sides

Corresponding congruent Side-Angle-Side

Corresponding congruent Side-Side-Angle

Corresponding congruent Angle-Side-Angle

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Problem 2

Student Task Statement

Here are some measurements for triangle and triangle :

Angle and angle are both 30°.
and both measure 6 units.
and both measure 4 units.

Lin thinks these triangles must be congruent. Priya says she knows they might not be congruent. Construct 2 triangles with the given measurements that aren't congruent. Explain why triangles with 3 congruent parts aren't necessarily congruent.

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Problem 3

ForLesson 9: Side-Side-Side Triangle Congruence

Student Task Statement

Jada states that diagonal bisects angles and . Is she correct? Explain your reasoning.

<p>Triangle WYZ and WYX. WZ is congruent to WX and YZ is congruent to YX. The triangles share side WY.</p>

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Problem 4

ForLesson 10: Practicing Proofs

Student Task Statement

Select all true statements based on the diagram.

<p>Quadrilateral ABCD. Line AB is parallel to line DC, both cut by congruent transversals AD and BC. Diagonals AC and DB bisect each other at point E at a right angle. Segment AE is congruent to segment BE.</p>

Angle is congruent to angle .

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Problem 5

ForLesson 9: Side-Side-Side Triangle Congruence

Student Task Statement

is a kite. Angle has a measure of 94 degrees, and angle has a measure of 112 degrees. Find the measure of angle .

<p>Kite W X Y Z. Diagonal W Y is drawn in. Sides Z W and W X have single tick marks. Sides X Y and Y Z have double tick marks.</p>

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Problem 6

ForLesson 8: The Perpendicular Bisector Theorem

Student Task Statement

Andre is thinking through a proof using a reflection to show that a triangle is isosceles given that its base angles are congruent. Complete the missing information for his proof.

<p>Triangle A C D. Angles D and C have arcs with single tick marks. Point B lies on side D C, and segment A B is drawn in.</p>

Construct such that is the perpendicular bisector of segment . We know angle is congruent to . is congruent to since is the perpendicular bisector of . Angle is congruent to angle because they are both right angles. Triangle is congruent to triangle because of the Triangle Congruence Theorem. is congruent to because they are corresponding parts of congruent triangles. Therefore, triangle is an isosceles triangle.

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Problem 7

ForLesson 3: Congruent Triangles, Part 1

Student Task Statement

The triangles are congruent. Which sequence of rigid motions takes triangle onto triangle ?

<p>Triangle ABC is congruent to triangle EDF.</p>

Translate using directed line segment . Rotate using as the center so that coincides with . Reflect across line .

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Lesson 11 Resources

Student Materials

Angle is congruent to angle .

Segment is congruent to segment .

Segment is congruent to segment .

Line is parallel to line .

Line is parallel to line .

Translate using directed line segment . Rotate using as the center so that coincides with . Reflect across line .

Translate using directed line segment . Rotate using as the center so that coincides with . Reflect across line .

Translate using directed line segment . Rotate using as the center so that coincides with . Reflect across line .