Unit 1, Lesson 9

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Integrated Math 1

Practice

Problem 1

Student Task Statement

Which construction can be used to determine whether point is closer to point or point ?

Practice

Construct triangle .
Construct a line perpendicular to segment through point .
Construct the bisector of angle .
Construct the perpendicular bisector of segment .

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Problem 2

Student Task Statement

The diagram is a straightedge and compass construction. Lines , , and are the perpendicular bisectors of the sides of triangle . Select all the true statements.

<p>Triangle A B C with intersecting lines. </p>

Point is closer to point than it is to point .

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Problem 3

Student Task Statement

Decompose the figure into regions that are closest to each vertex. Explain or show your reasoning.

<p>Two triangles, creating Quadrilateral D C A B. Triangle B C D on the left, Triangle A B C on the right. Both triangles share side B C.</p>

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Problem 4

Student Task Statement

Which construction could be used to construct an isosceles triangle given line segment ?

Mark a third point that is not on segment . Draw segments and .

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Problem 5

ForLesson 7: Construction Techniques 5: Squares

Student Task Statement

Select all true statements about regular polygons.

All angles are right angles.
All angles are congruent.
All side lengths are equal.
There are exactly 4 sides.
There are at least 3 sides.

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Problem 6

ForLesson 7: Construction Techniques 5: Squares

Student Task Statement

This diagram shows the beginning of a straightedge and compass construction of a rectangle.

The construction followed these steps:

<p>Three lines. Two vertical lines intersect a horizontal line at points A and B, making right angles. The horizontal line is on the bottom of the diagram. On the left line, point C is marked at the top.</p>

Start with two marked points and .
Use a straightedge to construct line .
Use a previous construction to construct a line perpendicular to passing through .
Use a previous construction to construct a line perpendicular to passing through .
Mark a point on the line perpendicular to passing through .

Explain the steps needed to complete this construction.

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Problem 7

ForLesson 5: Construction Techniques 3: Perpendicular Lines and Angle Bisectors

Student Task Statement

This diagram is a straightedge and compass construction of an angle bisector. Is it important that the circle with center passes through and that the circle with center passes through ? Show or explain your reasoning.

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Point is closer to point than it is to point .

Point is closer to point than it is to point or point .

Label a point on segment and construct a line perpendicular to through point . Draw segments and .

Construct the perpendicular bisector of segment . Mark the intersection of this line and and label it . Draw segments and .

Construct the perpendicular bisector of segment . Mark any point on the perpendicular bisector except where it intersects . Draw segments and .

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Practice

Problem 1

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Problem 2

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Problem 3

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Problem 4

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Problem 5

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Problem 6

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Problem 7

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Lesson 9 Resources