Sawtooth Middle School Remote Learning Cover Sheet

Subject: Honors Math 1 Grade Level: 8 Teacher Names: Funkhouser Date Range: 4/27 – 5/1 Day Learning Intention Description/Directions Monday I can determine if two lines are

parallel and write the equations of parallel lines.

Complete the worksheet for today. The answers are on the last page.

Tuesday I can determine if two lines are perpendicular and write the equations of perpendicular lines.

Complete the worksheet for today. The answers are on the last page.

Wednesday I can classify triangles based on their sides.

Complete the worksheet for today. The answers are on the last page.

Thursday I can determine if two triangles are congruent and describe the congruence.

Complete the worksheet for today. The answers are on the last page.

Friday I can prove when two triangles are congruent.

Complete the worksheet for today. The answers are on the last page.

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Monday, April 27 - Parallel Slopes Parallel Lines and Slopes Two lines in the same plane that never intersect are parallel lines. Two distinct nonvertical lines are parallel if and only if they have the same slope. All vertical lines are parallel. In Exercises 1–6, determine which of the lines, if any, are parallel. Explain.

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In Exercises 7 and 8, write an equation of the line that passes through the given point and is parallel to the given line.

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Tuesday, April 28 – Parallel and Perpendicular Slopes Perpendicular Lines and Slopes Two lines in the same plane that intersect to form right angles are perpendicular lines. Nonvertical lines are perpendicular if and only if their slopes are negative reciprocals. Vertical lines are perpendicular to horizontal lines. In Exercises 9–14, determine which of the lines, if any, are parallel or perpendicular. Explain.

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In Exercises 15 and 16, write an equation of the line that passes through the given point and is perpendicular to the given line.

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Wednesday, April 29 – Classifying Triangles

1. Identify the different types of triangles from the figure by naming them. EX: ∆𝑨𝑩𝑪 a.) isosceles triangles b.) scalene triangles

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2. Find x and the measure of each side of equilateral triangle RST.

3. Find 𝒙, 𝑱𝑴((((,𝑴𝑵(((((, 𝒂𝒏𝒅𝑱𝑵(((( if ∆𝑱𝑴𝑵 is an isosceles triangle with 𝑱𝑴(((( ≅ 𝑴𝑵(((((.

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𝟒.𝑲𝑳(((( is a segment representing one side of the isosceles right triangle KLM, with K(2,6), and L(4,2). ∠𝑲𝑳𝑴 is a right angle, and 𝑲𝑳(((( ≅ 𝑳𝑴(((((. Describe how to find the coordinates of vertex M and name these coordinates.

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Thursday, April 30 – Congruent Triangles Congruent Triangles: triangles that are the same size and shape.

• Each triangle has three angles and three sides. • If all of the corresponding parts of two triangles are the same, then the triangles are

congruent. • CPCTC – Corresponding parts of congruent triangles are congruent • If the sides of one triangle are congruent to the sides of a second triangle, then the

triangles are SSS congruent. • If two sides and the angle between the sides of one triangle are congruent to two sides

and the angle between the sides of another triangle, then the triangles are SAS congruent.

• If two angles and the side between the angles of one triangle are congruent to two angles and the side between the angles of another triangle, then the triangles are ASA congruent.

• If two angles and a non-included side of one triangle are congruent to the corresponding two angles and a side of a second triangle, then the two triangles are AAS congruent.

Congruent Triangles:

∆𝐴𝐵𝐶 ≅ ∆𝐸𝐹𝐺 Corresponding Congruent Angles:

∠𝐴 ≅ ∠𝐸 ∠𝐵 ≅ ∠𝐹 ∠𝐶 ≅ ∠𝐺

Corresponding Congruent Sides:

𝐴𝐵++++ ≅ 𝐸𝐹++++ 𝐵𝐶++++ ≅ 𝐹𝐺++++ 𝐴𝐶++++ ≅ 𝐸𝐺++++

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1. In the following figure, 𝑸𝑹(((((= 12, 𝑹𝑺(((( = 23, 𝑸𝑺(((( = 24, 𝑹𝑻(((( = 12, 𝑻𝑽(((( = 24, and 𝑹𝑽(((( = 23.

a) Name the corresponding congruent angles and sides. b) Name the congruent triangles.

For 2-17 state if the two triangles are congruent. If they are, state how you know. 2. 3. 4. 5. 6.

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7. 8. 9.

10. 11. 12. 13. 14. 15. 16. 17.

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Friday, May 1 – Proving Congruence Example for how to write a two-column proof.

Statements Reasons 1. 𝐷𝐺++++ ≅ 𝐸𝐺++++ 𝐵𝐺++++ ≅ 𝐶𝐺++++ ∠𝐷𝐺𝐵 ≅ ∠𝐸𝐺𝐶 2. ∆𝐵𝐷𝐺 ≅ ∆𝐶𝐸𝐺 3. 𝐷𝐵++++ ≅ 𝐸𝐶++++ ∠𝐷 ≅ ∠𝐸 ∠𝐵 ≅ ∠𝐶

1. Given (bisect definition) 2. SAS 3. CPCTC

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For 1-4 write a two-column proof. 1. 2.

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3. Given:∠𝑊&∠𝑌are right angles; ∠𝑉𝑋𝑊 ≅ ∠𝑍𝑋𝑌; 𝑋is the midpoint of 𝑊𝑌*****

Prove: ∆𝑉𝑊𝑋 ≅ ∆𝑍𝑌𝑋 4.

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ANSWERS 4/27 1. a & c 2. a & c 3. a & c 4. NONE 5. b & c 6. a & b m = 3 m = -2 m = ½ m = − !

" m = #

$

7.𝑦 = #

!𝑥 − 2 8. 𝑦 = −2𝑥

4/28 9. a & c 10. a & b 11. NONE 12. a & b 13. a & b 14. a & c Parallel perp. Parallel perp. parallel m = -2 m = 3 & − #

! m = 3 m = !

" & − "

! m = %

$

15. 𝑦 = − !

%𝑥 − 1 16. 𝑦 = − #

%𝑥 + $

%

4/29 1.a) ∆𝐴𝐵𝐷, ∆𝐵𝐷𝐸 1.b) ∆𝐴𝐵𝐶, ∆𝐴𝐶𝐷, ∆𝐵𝐶𝐸, ∆𝐶𝐷𝐸, ∆𝐴𝐷𝐸, ∆𝐴𝐵𝐸 2. 𝑋 = 9 3. 𝑥 = 4 4. (2,2) OR (4,6) Segments = 18 𝐽𝑀++++&𝑀𝑁+++++ = 3 𝐽𝑁++++ = 2 4/30 1. a) 𝑄𝑅++++ ≅ 𝑇𝑅++++ , 𝑄𝑆++++ ≅ 𝑇𝑉++++, 𝑅𝑆++++ ≅ 𝑅𝑉++++ , ∠𝑄 ≅ ∠𝑇 , ∠𝑄𝑅𝑆 ≅ ∠𝑇𝑅𝑉 , ∠𝑆 ≅ ∠𝑉

1. b) ∆𝑄𝑅𝑆 ≅ ∆𝑇𝑅𝑉 , SSS 2. SSS 3. AAS 4. NOT CONGRUENT 5. ASA 6. SSS 7. SAS 8. SAS 9. ASA 10. AAS 11. NOT CONGRUENT 12. SAS 13. SAS 14. ASA 15. AAS 16. NOT CONGRUENT 17. SAS

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5/1 1. 2.

Statements Reasons 1. 𝐴𝐵++++ ≅ 𝐴𝐶++++ 𝐵𝑌++++ ≅ 𝐶𝑌++++ 2. 𝐴𝑌++++ ≅ 𝐴𝑌++++ 3. ∆𝐵𝑌𝐴 ≅ ∆𝐶𝑌𝐴 4. ∠𝐵 ≅ ∠𝐶 ∠𝐵𝐴𝑌 ≅ ∠𝐶𝐴𝑌 ∠𝐴𝑌𝐵 ≅ ∠𝐴𝑌𝐶

1. Given 2. Shared side 3. SSS 4. CPCTC

3. 4.

Statements Reasons 1. ∠𝑊 ≅ ∠𝑌 ∠𝑉𝑋𝑊 ≅ ∠𝑍𝑋𝑌 𝑊𝑋+++++ ≅ 𝑌𝑋++++ 2. ∆𝑉𝑊𝑋 ≅ ∆𝑍𝑌𝑋 3. 𝑉𝑋++++ ≅ 𝑍𝑋++++ 𝑉𝑊+++++ ≅ 𝑍𝑌++++ ∠𝑉 ≅ ∠𝑍

1. Given 2. ASA 3. CPCTC