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9-12 Integrated Math 1 Unit 2 Lesson 9

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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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9-12

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

Modeling Prompts

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Lesson 2
Lesson 3
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Lesson 11

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Unit 2, Lesson 9

Side-Side-Side Triangle Congruence

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Integrated Math 1

Practice

Problem 1
Student Task Statement

A kite is a quadrilateral which has 2 sides next to each other that are congruent and where the other 2 sides are also congruent. Given kite , show that at least one of the diagonals of a kite decomposes the kite into 2 congruent triangles.

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Problem 2

Student Task Statement

Mai has proven that triangle is congruent to triangle using the Side-Side-Side Triangle Congruence Theorem. Why can she now conclude that diagonal bisects angles and ?

<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 3

Student Task Statement

is a kite. Angle has a measure of 133 degrees, and angle has a measure of 60 degrees. Find the measure of angle .

<p>Kite WXYZ. WX is congruent to WZ and XY is congruent to ZY.</p>

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Problem 4

ForLesson 8: The Perpendicular Bisector Theorem

Student Task Statement

Each statement is always true. Select all statements for which the converse is also always true.

Statement: If 2 angles form a straight angle, then they are supplementary. Converse: If 2 angles are supplementary, then they form a straight angle.
Statement: If a triangle is isosceles, then the base angles are congruent. Converse: If the base angles of a triangle are congruent, then the triangle is isosceles.
Statement: If a point is equidistant from the 2 endpoints of a segment, then it lies on the perpendicular bisector of the segment. Converse: If a point lies on the perpendicular bisector of a segment, then it is equidistant from the 2 endpoints of the segment.
Statement: If 2 angles are vertical, then they are congruent. Converse: If 2 angles are congruent, then they are vertical.
Statement: If 2 lines are perpendicular, then they intersect to form 4 right angles. Converse: If 2 lines intersect to form 4 right angles, then the 2 lines are perpendicular.

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Problem 5

ForLesson 7: Angle-Side-Angle Triangle Congruence

Student Task Statement

Prove triangle is congruent to triangle .

<p>Line DC is parallel to and above line AB and cut by transversal DB. Angles A and C are right angles.</p>

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Problem 6

ForLesson 6: Side-Angle-Side Triangle Congruence

Student Task Statement

Triangles and are isosceles. Angle has a measure of 84 degrees, and angle has a measure of 24 degrees. Find the measure of angle .

<p>Triangle A C D, isosceles, point B inside. Side A D and A C have one tick mark. Segments B D, B C, and BA are drawn. Triangle B C D is isosceles. Sides B D and B C have two tick marks.</p> — and

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Problem 7

ForLesson 1: Congruent Parts, Part 1

Student Task Statement

Reflect right triangle across line . Classify triangle according to its side lengths. Explain how you know.

<p>Triangle ABC with angle ABC marked as a right angle.</p>

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Lesson 9 Resources

Student Materials Student Materials in Spanish