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9-12 Geometry Unit 7 Lesson 1

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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

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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

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

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

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Unit 7, Lesson 1

Lines, Angles, and Curves

Geometry

Practice

Problem 1

Find the measures of \(x, y,\) and \(z\).

<p>Circle with center A.</p>

Problem 2

Give an example from the image of each kind of segment.

a diameter
a chord that is not a diameter
a radius

<p>Circle with center A.</p>

Problem 3

Identify whether each statement must be true, could possibly be true, or definitely can’t be true.

A diameter is a chord.
A radius is a chord.
A chord is a diameter.
A central angle measures 90\(^\circ\).

Problem 4

ForLesson 17: Lines in Triangles

Write an equation of the altitude from vertex \(A\).

<p>Triangle ABC graphed. A = 2 comma 1, B = -1 comma 4, C = 8 comma 2. altitude drawn from vertex A to side BC.</p>

Problem 5

ForLesson 16: Weighted Averages in a Triangle

Triangle \(ABC\) has vertices at \((5,0), (1,6),\) and \((9,3)\). What is the point of intersection of the triangle’s medians?

The medians do not intersect at a single point.
\((3,3)\)
\((5,3)\)
\((3,4.5)\)

Problem 6

ForLesson 15: Weighted Averages

Consider the parallelogram with vertices at \((0,0), (8,0), (4,6),\) and \((12,6)\). Where do the diagonals of this parallelogram intersect?

Problem 7

ForLesson 10: Parallel Lines in the Plane

Lines \(\ell\) and \(p\) are parallel. Select all true statements.

<p><span class="math">\(\text{Parallel lines }l \text{ and }p \text{ on a coordinate plane, origin } O\)</span></p>

Triangle \(ADB\) is congruent to triangle \(CEF\).
The slope of line \(\ell\) is equal to the slope of line \(p\).
Triangle \(ADB\) is similar to triangle \(CEF\).
\(\sin(A) = \sin(C)\)
\(\cos(B) = \sin(C)\)

Problem 8

ForLesson 7: Angle-Side-Angle Triangle Congruence

Mai wrote a proof that triangle \(AED\) is congruent to triangle \(CEB\). Mai's proof is incomplete. How can Mai fix her proof?

We know side \(AE\) is congruent to side \(CE\) and angle \(A\) is congruent to angle \(C\). By the Angle-Side-Angle Triangle Congruence Theorem, triangle \(AED\) is congruent to triangle \(CEB\).

<p>Triangles ADE and CBE meet only at point E. Angles A and C are congruent. Sides AE and CE are congruent.</p> — \(\angle A \cong \angle C, \overline{AE} \cong \overline{CE}\)