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9-12 Geometry Unit 2 Lesson 14

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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 Lesson 15

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Lesson 3
Lesson 4
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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 14

Bisect It

Geometry

Practice

Problem 1

Select all quadrilaterals for which a diagonal is also a line of symmetry.

trapezoid
isosceles trapezoid
parallelogram
rhombus
rectangle
square

to access Practice Problem Solutions.

Problem 2

Show that diagonal \(EG\) is a line of symmetry for rhombus \(EFGH\).

<p>Rhombus E F G H. Line E G is drawn in the middle of the rhombus.</p>

to access Practice Problem Solutions.

Problem 3

ForLesson 13: Proofs about Parallelograms

\(ABDE\) is an isosceles trapezoid. Priya makes a claim that triangle \( AEB\) is congruent to triangle \(DBE\). Convince Priya this is not true.

<p>Isosceles trapezoid A B D E. Angles are marked with tick marks, as follows: D E A, one mark; E A B, two marks; A B D, two tick marks; B D E, one tick mark. Segment A E and B D each have one tick mark.<br>
</p> — \(\overline{AE} \cong \overline{BD} , \angle A \cong \angle B , \angle E \cong \angle D\)

Problem 4

ForLesson 13: Proofs about Parallelograms

In quadrilateral \(ABCD\), triangle \(ADC\) is congruent to \(CBA\). Show that \(ABCD\) is a parallelogram.

<p>Quadrilateral ABCD with line segment AC.</p>

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Problem 5

ForLesson 12: Proofs about Quadrilaterals

Priya is convinced the diagonals of the isosceles trapezoid are congruent. She knows that if she can prove triangles that include the diagonals congruent, then she will show that diagonals are also congruent. Help her complete the proof.

\(ABDE\) is an isosceles trapezoid.

<p>Isosceles trapezoid A B D E. Angles are marked with tick marks, as follows: D E A, one mark; E A B, two marks; A B D, two tick marks; B D E, one tick mark. Segment A E and B D each have one tick mark.<br>
</p> — \(\overline{AE} \cong \overline{BD} , \angle A \cong \angle B , \angle E \cong \angle D\)

Draw auxiliary lines that are diagonals \(\underline{\hspace{.5in}1\hspace{.5in}}\) and \(\underline{\hspace{.5in}2\hspace{.5in}}\). \(AB \) is congruent to \(\underline{\hspace{.5in}3\hspace{.5in}}\)because they are the same segment. We know angle \(B\) and \(\underline{\hspace{.5in}4\hspace{.5in}}\) are congruent. We know \(AE\) is congruent to \(\underline{\hspace{.5in}5\hspace{.5in}}\). Therefore, triangle \(ABE \) and \(\underline{\hspace{.5in}6\hspace{.5in}}\) are congruent because of \(\underline{\hspace{.5in}7\hspace{.5in}}\). Finally, diagonal \(BE\) is congruent to \(\underline{\hspace{.5in}8\hspace{.5in}}\) because \(\underline{\hspace{.5in}9\hspace{.5in}}\).

Problem 6

ForLesson 11: Side-Side-Angle (Sometimes) Congruence

Is triangle \(AFE\) congruent to triangle \(ADE\)?
Explain your reasoning.

<p>Triangle A F D. Segment A E, with E on F D. A F and A D have single tick marks. Angles F and D have arcs with single tick marks.</p> — \(\overline{AF} \cong \overline{AD}, \angle F \cong \angle D\)

Problem 7

ForLesson 6: Side-Angle-Side Triangle Congruence

Triangle \(DAC\) is isosceles, with congruent sides \(AD\) and \(AC\). Which additional given information is sufficient for showing that triangle \(DBC\) is isosceles? Select all that apply.

<p>Triangle ACD with point B near the center. Line segment AC is congruent to AD.</p>

Lesson 14 Resources

Student Materials

to access Practice Problem Solutions.

to access Practice Problem Solutions.

to access Practice Problem Solutions.

Segment \(DB\) is congruent to segment \(BC\).
Segment \(AB\) is congruent to segment \(BD\).
Angle \(ABD\) is congruent to angle \(ABC\).
Angle \(ADC\) is congruent to angle \(ACD\).
\(AB\) is an angle bisector of \(DAC\).
Triangle \(BDA\) is congruent to triangle \(BDC\).

to access Practice Problem Solutions.

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