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# Geometry Unit 4 Note Sheets Date Name of Lesson...

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Geometry Unit 4 Note Sheets 1 Date Name of Lesson Classifying Triangles 4.1 Angles of Triangles 4.2 Inequalities in One Triangle 5.3 Constructing Incenter (Angle Bisectors) Constructing Circumcenter (Perpendicular Bisectors) 5.1, 5.2 Congruent Triangles 4.3 Quiz Proving Triangles Congruent SSS, SAS, ASA, AAS, HL 4.4, 4.5 Use http://www.mathopenref.com/congruentaaa.html to show why AAA doesn’t work Use http://www.mathopenref.com/congruentssa.html to show why ASS doesn’t work Quiz Isosceles and Equilateral Triangles 4.6 Congruence Transformations 4.7 Practice Test Unit Test
Transcript

Geometry Unit 4 Note Sheets

1

Date Name of Lesson

Classifying Triangles 4.1

Angles of Triangles 4.2

Inequalities in One Triangle 5.3

Constructing Incenter (Angle Bisectors)

Constructing Circumcenter (Perpendicular Bisectors)

5.1, 5.2

Congruent Triangles 4.3

Quiz

Proving Triangles Congruent – SSS, SAS, ASA, AAS, HL 4.4, 4.5

Use http://www.mathopenref.com/congruentaaa.html to show why AAA doesn’t work

Use http://www.mathopenref.com/congruentssa.html to show why ASS doesn’t work

Quiz

Isosceles and Equilateral Triangles 4.6

Congruence Transformations 4.7

Practice Test

Unit Test

Geometry Unit 4 Note Sheets

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4.1 Classifying Triangles Notes

Guided Practice

1. Classify each triangle by their angles.

2.

Guided Practice

Classify each triangle by their sides.

3. 4.

Classify each triangle by their sides.

5. ∆𝐴𝐵𝐶

6. ∆𝐵𝐷𝐶

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Guided Practice

7. If point 𝑀 is the midpoint of 𝐽�̅�, classify ∆𝐽𝐾𝑀 as equilateral, isosceles, or scalene. Explain your reasoning.

8. If 𝑌 is the midpoint of 𝑉𝑋̅̅ ̅̅ , and 𝑊𝑌 = 3.0 𝑢𝑛𝑖𝑡𝑠, classify ∆𝑉𝑊𝑌 as equilateral, isosceles, or scalene.

Guided Practice

9. Find the measures of the sides of isosceles triangle 𝐴𝐵𝐶.

10. Find the measures of the sides of the isosceles triangle 𝐾𝐿𝑀 with base 𝐾𝐿̅̅ ̅̅ .

Geometry Unit 4 Note Sheets

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4.2 Angles of Triangles Notes

Guided Practice

Find the measure of the numbered angles.

1. 2.

3. 4.

Geometry Unit 4 Note Sheets

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Guided Practice

5. Find the measure of ∠𝐹𝐿𝑊. 6. Find the measures of the numbered angles.

7. Find the measure of the exterior angle shown. 8. Find the measures of the numbered angles.

Geometry Unit 4 Note Sheets

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Guided Practice

Is it possible to form a triangle with the given side lengths? If not, explain why not.

1. 5 cm, 7 cm, 10 cm 2. 3 in, 4 in, 8 in

3. 6 m, 14 m, 10 m

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Guided Practice

Compare the given measures.

Geometry Unit 4 Note Sheets

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5.3 Inequalities in One Triangle

Guided Practice

1. Use the exterior angle theorem to name angles that have measures less than 𝑚∠4.

2. Use the exterior angle theorem to name angles that have measures less than 𝑚∠7.

3. Use the exterior angle theorem to name angles that have measures less than 𝑚∠2.

4. Use the exterior angle theorem to name angles that have measures less than 𝑚∠9.

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Guided Practice

List the angles and sides of each triangle in order from smallest to largest.

1. 2.

3. 4.

Guided Practice

List the angles and sides of each triangle in order from smallest to largest.

5. 6.

Geometry Unit 4 Note Sheets

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5.1, 5.2 Constructing Incenter (Angle Bisectors)

Guided Practice

1. Construct the angle bisector of each angle to find the Incenter. (Draw circle inside with the center at the

incenter.)

Geometry Unit 4 Note Sheets

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5.1, 5.2 Constructing Incenter (Angle Bisectors)

Guided Practice

1. Construct the perpendicular bisector of each angle to find the Circumcenter. (Draw circle around the outside

with the center at the circumcenter.)

Geometry Unit 4 Note Sheets

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4.3 Congruent Triangles Notes

Guided Practice

1. Show that the polygons are congruent by identifying all the congruent corresponding parts. Then write a

congruence statement.

2.

Geometry Unit 4 Note Sheets

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Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

Guided Practice

3. In the diagram ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐹𝐸. 4. In the figure, ∆𝐿𝑀𝑁 ≅ ∆𝑄𝑅𝑆.

Find the values of 𝑥 and 𝑦. Find the values of 𝑥 and 𝑦.

5. In the diagram ∆𝐼𝑇𝑃 ≅ ∆𝑁𝐺𝑂. Find the values of 𝑥 and 𝑦.

Geometry Unit 4 Note Sheets

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6. 7.

Geometry Unit 4 Note Sheets

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4.4, 4.5 Proving Triangles Congruent – SSS, SAS, ASA, AAS, HL Notes

Side-Side-Side (SSS) Congruence

Side-Angle-Side (SAS) Congruence

Angle-Side-Angle (ASA) Congruence

Angle-Angle -Side (AAS) Congruence

Hypotenuse-Leg (HL) Congruence

Guided Practice

Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove

congruence, write not possible.

1. 2. 3.

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4. 5. 6.

7. 8. 9.

Guided Practice

Use the Distance Formula and SSS Congruence Postulate to show that ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹.

10.

11.

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4.6 Isosceles and Equilateral Triangles Notes

Guided Practice

1. Name two unmarked congruent angles.

2. Name two unmarked congruent segments.

3. Name two unmarked congruent angles.

4. Name two unmarked congruent segments.

Geometry Unit 4 Note Sheets

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Guided Practice

5. Find each measure.

𝑚∠𝑌

𝑌𝑍

6. Find each measure.

𝑚∠𝑀

𝑃𝑁

Guided Practice

7. Find the value of x.

8. Find the value of y.

9. Find the value of x.

10. Find the value of y.

Guided Practice

Find the value of each variable.

11. 12.

13. 14.

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Use SAS to prove triangles

congruent.

4.7 Congruence transformations

Use SSS to prove triangles

congruent.

Geometry Unit 4 Note Sheets

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5. Graph A(2,2), B(4, 7), C(6,2) and D(2,-2), F(4, -7), G(6, -2) on the same axis. Identify transformation

and prove triangles are congruent.

6. Determine whether ∆𝑻𝑱𝑫 ≅ ∆𝑺𝑬𝑲 given T(-4, -2), J(0, 5), D(1, -1), S(-1, 3), E(3, 10),

and K(4, 4). Explain and identify transformation. (Verify by using SSS,SAS,ASA, HL or AAS)

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