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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

Modeling Prompts

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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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9-12

Algebra 1
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Algebra 2
Extra Support Materials for Algebra 1

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

Modeling Prompts

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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 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

Problem 2

Show that diagonal is a line of symmetry for rhombus .

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

Problem 3

ForLesson 13: Proofs about Parallelograms

is an isosceles trapezoid. Priya makes a claim that triangle is congruent to triangle . 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>

Problem 4

ForLesson 13: Proofs about Parallelograms

In quadrilateral , triangle is congruent to . Show that is a parallelogram.

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

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.

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>

Draw auxiliary lines that are diagonals and . is congruent to because they are the same segment. We know angle and are congruent. We know is congruent to . Therefore, triangle and are congruent because of . Finally, diagonal is congruent to because .

Problem 6

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

Is triangle congruent to triangle ?
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>

Problem 7

ForLesson 6: Side-Angle-Side Triangle Congruence

Triangle is isosceles, with congruent sides and . Which additional given information is sufficient for showing that triangle is isosceles? Select all that apply.

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

Segment is congruent to segment .

Segment is congruent to segment .

Angle is congruent to angle .

Angle is congruent to angle .

is an angle bisector of .

Triangle is congruent to triangle .