Share this document with a friend

20

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

2

4.1 Classifying Triangles Notes

Guided Practice

1. Classify each triangle by their angles.

Your Turn

2.

Guided Practice

Classify each triangle by their sides.

3. 4.

Your Turn

Classify each triangle by their sides.

5. ∆𝐴𝐵𝐶

6. ∆𝐵𝐷𝐶

Geometry Unit 4 Note Sheets

3

Guided Practice

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

Your Turn

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

Explain your reasoning.

Guided Practice

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

Your Turn

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

Geometry Unit 4 Note Sheets

4

4.2 Angles of Triangles Notes

Guided Practice

Find the measure of the numbered angles.

1. 2.

Your Turn

3. 4.

Geometry Unit 4 Note Sheets

5

Guided Practice

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

Your Turn

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

Geometry Unit 4 Note Sheets

6

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

Your Turn

3. 6 m, 14 m, 10 m

Geometry Unit 4 Note Sheets

8

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.

Your Turn

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.

Geometry Unit 4 Note Sheets

9

Guided Practice

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

1. 2.

Your Turn

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

10

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

11

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

12

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

13

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.

Your Turn

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

Geometry Unit 4 Note Sheets

15

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.

Geometry Unit 4 Note Sheets

16

Your Turn

4. 5. 6.

7. 8. 9.

Guided Practice

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

10.

Your Turn

11.

Geometry Unit 4 Note Sheets

17

4.6 Isosceles and Equilateral Triangles Notes

Guided Practice

1. Name two unmarked congruent angles.

2. Name two unmarked congruent segments.

Your Turn

3. Name two unmarked congruent angles.

4. Name two unmarked congruent segments.

Geometry Unit 4 Note Sheets

18

Guided Practice

5. Find each measure.

𝑚∠𝑌

𝑌𝑍

Your Turn

6. Find each measure.

𝑚∠𝑀

𝑃𝑁

Guided Practice

7. Find the value of x.

8. Find the value of y.

Your Turn

9. Find the value of x.

10. Find the value of y.

Guided Practice

Find the value of each variable.

11. 12.

Your Turn

13. 14.

Geometry Unit 4 Note Sheets

19

Use SAS to prove triangles

congruent.

4.7 Congruence transformations

Use SSS to prove triangles

congruent.

Geometry Unit 4 Note Sheets

20

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)

Recommended